[Bug]: Pushing image to a private registry fails

### I have done the following

- [x] I have searched the existing issues
- [ ] If possible, I've reproduced the issue using the 'main' branch of this project

### Steps to reproduce

I struggle with pushing to a registry.

Done via Screen Sharing login via Terminal.app, `container` installed from `brew`.
```
$ container r login harbor-registry.internal
Provide registry username harbor-registry.internal: admin
Provide registry password:
Login succeeded
```

Then push fails with:
```
Error: error querying keychain for harbor-registry.internal (cause: "queryError("query failure: unhandledError(status: -25308)")")
```

There are no pop ups for password access.

Logs:

```
$ log stream --predicate 'subsystem == "com.apple.securityd"' --level debug
[...]
2026-03-13 08:02:56.301176+0200 0x27c0cb9 Default 0x433fcf6 36833 0 container-core-images: (Security) [com.apple.securityd:thread-local-client-debug] SecSecurityClientGet new thread!
2026-03-13 08:02:56.301315+0200 0x27c0cb9 Debug 0x433fcf6 36833 0 container-core-images: (Security) [com.apple.securityd:xpc] flagAlways:false inEduMode:false flagOld:false
2026-03-13 08:02:56.301339+0200 0x27c0cb9 Debug 0x433fcf6 36833 0 container-core-images: (Security) [com.apple.securityd:xpc] not using system keychain
2026-03-13 08:02:56.302272+0200 0x27c088f Debug 0x433fcf6 42953 0 secd: [com.apple.securityd:serverxpc] XPC [container-core-i[36833]/1#-1 LF=0] operation: copy_matching (1)
[...]
2026-03-13 08:02:56.321444+0200 0x27bd978 Default 0x0 162 0 securityd: [com.apple.securityd:clientid] code requirement check failed (-67050), client is not Apple-signed
2026-03-13 08:02:56.321461+0200 0x27bd978 Default 0x0 162 0 securityd: [com.apple.securityd:SecurityAgentConnection] activate(0x16b8160a0)
2026-03-13 08:02:56.321518+0200 0x27bd978 Default 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] MacOS error: -25337
2026-03-13 08:02:56.321756+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 0 Security 0x00000001914ea8b8 Security::CommonError::LogBacktrace() + 124
2026-03-13 08:02:56.321776+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 1 Security 0x00000001914eae50 Security::MacOSError::MacOSError(int) + 312
2026-03-13 08:02:56.321788+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 2 Security 0x00000001914eaec0 Security::MacOSError::throwMe(int) + 40
2026-03-13 08:02:56.321798+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 3 Security 0x00000001914e8838 Security::makeCFArray(long, ...) + 0
2026-03-13 08:02:56.321806+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 4 Security 0x0000000191454ad4 cssmErrorString + 344
2026-03-13 08:02:56.321815+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 5 securityd 0x00000001047f3cb0 securityd + 441520
2026-03-13 08:02:56.321823+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 6 securityd 0x00000001047f3dc4 securityd + 441796
2026-03-13 08:02:56.321832+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 7 securityd 0x00000001047db0c8 securityd + 340168
2026-03-13 08:02:56.321841+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 8 securityd 0x00000001047dcce4 securityd + 347364
2026-03-13 08:02:56.321849+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 9 securityd 0x00000001047ddba8 securityd + 351144
2026-03-13 08:02:56.321857+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 10 securityd 0x00000001047ab904 securityd + 145668
2026-03-13 08:02:56.321866+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 11 securityd 0x00000001047aa7dc securityd + 141276
2026-03-13 08:02:56.321892+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 12 securityd 0x000000010479554c securityd + 54604
2026-03-13 08:02:56.321908+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 13 securityd 0x0000000104796f54 securityd + 61268
2026-03-13 08:02:56.321932+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 14 securityd 0x00000001047f1480 securityd + 431232
2026-03-13 08:02:56.321950+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 15 securityd 0x00000001047d2db4 securityd + 306612
2026-03-13 08:02:56.321980+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 16 securityd 0x00000001047cc948 securityd + 280904
2026-03-13 08:02:56.321997+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 17 securityd 0x00000001047e38c4 securityd + 374980
2026-03-13 08:02:56.322020+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 18 securityd 0x00000001047891d0 securityd + 4560
2026-03-13 08:02:56.322036+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 19 securityd 0x000000010478db0c securityd + 23308
2026-03-13 08:02:56.322060+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 20 securityd 0x00000001047e8b44 securityd + 396100
2026-03-13 08:02:56.322072+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 21 securityd 0x000000010478d208 securityd + 21000
2026-03-13 08:02:56.322101+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 22 libsystem_pthread.dylib 0x000000018d8edc08 _pthread_start + 136
2026-03-13 08:02:56.322117+0200 0x27bd978 Debug 0x0 162 0 securityd: (Security) [com.apple.securityd:security_exception] 23 libsystem_pthread.dylib 0x000000018d8e8ba8 thread_start + 8
2026-03-13 08:02:56.322174+0200 0x27bd978 Default 0x0 162 0 securityd: [com.apple.securityd:security_exception] CSSM Exception: 224 unknown error 224=e0
2026-03-13 08:02:56.322215+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 0 securityd 0x00000001047e9440 securityd + 398400
2026-03-13 08:02:56.322223+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 1 securityd 0x00000001047f3d54 securityd + 441684
2026-03-13 08:02:56.322232+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 2 securityd 0x00000001047f3dc4 securityd + 441796
2026-03-13 08:02:56.322239+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 3 securityd 0x00000001047db0c8 securityd + 340168
2026-03-13 08:02:56.322247+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 4 securityd 0x00000001047dcce4 securityd + 347364
2026-03-13 08:02:56.322254+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 5 securityd 0x00000001047ddba8 securityd + 351144
2026-03-13 08:02:56.322280+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 6 securityd 0x00000001047ab904 securityd + 145668
2026-03-13 08:02:56.322295+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 7 securityd 0x00000001047aa7dc securityd + 141276
2026-03-13 08:02:56.322319+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 8 securityd 0x000000010479554c securityd + 54604
2026-03-13 08:02:56.322334+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 9 securityd 0x0000000104796f54 securityd + 61268
2026-03-13 08:02:56.322365+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 10 securityd 0x00000001047f1480 securityd + 431232
2026-03-13 08:02:56.322380+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 11 securityd 0x00000001047d2db4 securityd + 306612
2026-03-13 08:02:56.322404+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 12 securityd 0x00000001047cc948 securityd + 280904
2026-03-13 08:02:56.322418+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 13 securityd 0x00000001047e38c4 securityd + 374980
2026-03-13 08:02:56.322443+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 14 securityd 0x00000001047891d0 securityd + 4560
2026-03-13 08:02:56.322457+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 15 securityd 0x000000010478db0c securityd + 23308
2026-03-13 08:02:56.322486+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 16 securityd 0x00000001047e8b44 securityd + 396100
2026-03-13 08:02:56.322510+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 17 securityd 0x000000010478d208 securityd + 21000
2026-03-13 08:02:56.322526+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 18 libsystem_pthread.dylib 0x000000018d8edc08 _pthread_start + 136
2026-03-13 08:02:56.322551+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:security_exception] 19 libsystem_pthread.dylib 0x000000018d8e8ba8 thread_start + 8
2026-03-13 08:02:56.322620+0200 0x27bd978 Default 0x0 162 0 securityd: [com.apple.securityd:SecurityAgentXPCQuery] SecurityAgentXPCQuery(0x16b8160a0) dying
2026-03-13 08:02:56.322629+0200 0x27bd978 Default 0x0 162 0 securityd: [com.apple.securityd:SecurityAgentConnection] SecurityAgentConnection(0x16b8160a0) dying
2026-03-13 08:02:56.322675+0200 0x27bd978 Debug 0x0 162 0 securityd: [com.apple.securityd:machserver] end request
2026-03-13 08:02:56.322884+0200 0x27c0cb9 Default 0x433fcf5 36833 0 container-core-images: (Security) [com.apple.securityd:security_exception] CSSM Exception: -2147415840 CSSMERR_CSP_NO_USER_INTERACTION
```

Similar to https://github.com/apple/container/issues/816, except this is to push which sometimes works.

### Current behavior

Failure to push the image to the registry.

### Expected behavior

Succesful push to the registry.

### Environment

```markdown
- OS: 26.2 / 26.3
- Container: 0.10.0
```

### Relevant log output

```shell
N/A
```

### Code of Conduct

- [x] I agree to follow this project's Code of Conduct

Start by reproducing the `container r login harbor-registry.internal` and image push sequence from the issue, then inspect the container CLI's registry credential and macOS keychain path. Compare the failure with the `com.apple.securityd` log output, especially the unhandled keychain error and missing password-access prompt. Done means pushing to the private registry succeeds without the keychain query failure.

Written by the indexing model from the issue text.