[Bug]: Wallet API - Solana Sign and Send triggers the Permissions screen when we already gave dapp Permissions

### Describe the bug

Solana Sign and Send triggers the Permissions screen, no matter if I'm already connected.
The Sign and Send request is never displayed

### Expected behavior

- If we are already connected to the dapp, we shouldn't trigger the Permissions screen.
- We should see the Sign and Send SOL screen

### Screenshots/Recordings

https://github.com/user-attachments/assets/10d1f171-23b0-46eb-b972-2c02c630fee9

### Steps to reproduce

1. Open the inner browser
2. Go to https://metamask.github.io/test-dapp-solana/latest/
3. Connect an Account with Solana network permissions
4. Click Sign Transaction --> see the tx is correctly displayed
5. Click Sign and Send Transaction --> see permissions screen is triggered
6. Accept again the permissions
7. See nothing else happens

### Error messages or log output

```shell

```

### Where was this bug found?

Internal release testing

### Version

7.76.0

### Build number

4532

### Build type

None

### Device

Pixel 6

### Operating system

Android

### Additional context

_No response_

### Severity

_No response_

Reproduce the flow in the inner browser with the Solana test dapp at metamask.github.io/test-dapp-solana/latest/, following the listed connection, Sign Transaction, and Sign and Send steps. Trace the Wallet API Sign and Send path and compare its permission handling with Sign Transaction. Done means an already connected dapp opens the Sign and Send SOL screen without another permission prompt.

Written by the indexing model from the issue text.