Lost OTK, leading to "OneTime key already exists" error and later UTDs

From time to time, we have reports from users whose clients get stuck uploading one-time-keys. For example:

```
2025-11-19T14:34:14.225Z D FetchHttpApi: --> POST https://matrix-client.matrix.org/_matrix/client/v3/keys/upload
2025-11-19T14:34:14.291Z D FetchHttpApi: <-- POST https://matrix-client.matrix.org/_matrix/client/v3/keys/upload [65ms 400]
2025-11-19T14:34:14.292Z D [Perf]: Make outgoing request 0 took 67ms
2025-11-19T14:34:14.292Z E Failed to process outgoing request 0: M_UNKNOWN: MatrixError: [400] One time key signed_curve25519:AAAAAAAAAEI already exists. Old key: {"key":"PUkTd3MCEG7a3g31uNH9uDfRbge5YHDZNgaHsL3QgwQ","signatures":{"@:matrix.org":{"ed25519:BRVTMXTHXB":"EemfO4mo2DGRqwttOK4WH0gO74RhudsN6/8v+hT0nUf+ZLQiUiku1D2dIYP09UibnN4ccKau4OCS7/FiCrjdDA"}}}; new key: {'key': 't/NppgUETPyrtUo9xprfu7pYoAnUOskwjVhPZ2Wz9xk', 'signatures': {'@:matrix.org': {'ed25519:BRVTMXTHXB': '+pstgfNA9s2I9KNNK+uHxeO/yclsfmPSIHn1jCMsom/pN7+9U/aScyKcS0y7apmUqROSUdh/RpQTkrbpSJRUDQ'}}} (https://matrix-client.matrix.org/_matrix/client/v3/keys/upload)
```

This very strongly suggests that the client has uploaded a one-time-key and then forgotten about it. It then creates a new OTK with the same ID; the client is then unable to upload further OTKs until the forgotten one is claimed by another device; and once it is claimed by another device, the resultant messages will be undecryptable.

Start by tracing the client code responsible for the /_matrix/client/v3/keys/upload request shown in the logs, then inspect how one-time-key state is retained after an upload. Done means the client does not reuse a lost key ID, does not remain blocked from uploading further keys, and does not cause undecryptable messages after a key is claimed.

Written by the indexing model from the issue text.