feat: Improved initial prompt handling

[35C4n0r]

Example - Opencode agent:

running -> stable (we send initial prompt on first stable) -> running (this is the part where it finally shows the splash screen and the agent is ready to accept input).

The PR tries to fix this by taking into account whether the input box is visible or not.

[github-actions]

✅ Preview binaries are ready!

To test with modules: agentapi_version = "agentapi_142" or download from: https://github.com/coder/agentapi/releases/tag/agentapi_142

[hugodutka]

Please add a test in conversation_test.go to check if the new logic behaves correctly.

[35C4n0r]

resolved all the comments.

[35C4n0r]

@mafredri resolved all the comments.