## Why
Reusing an MCP connection that is still starting after its
`startup_timeout_sec` changes leaves the old startup budget in effect.
## What changed
- Track the effective startup timeout on each MCP connection.
- Reuse a pending startup only when its timeout still matches the current
configuration.
- Continue reusing ready connections when only the startup timeout changes.
## Testing
Added integration coverage that refreshes the timeout while one server is
still initializing and another is ready, verifying that only the pending
startup is replaced.
GitOrigin-RevId: 5ed71a57d3bf0dd6e227aacd16acd3a35bc37ecf