fix: refresh Claude live config after common updates during takeover

[mydelren]

Summary

• refresh active Claude live settings after common-config updates while takeover is already active
• build the takeover backup snapshot from the in-flight common-config snippet instead of reloading the old stored snippet
• add a regression test covering common-config updates during active Claude takeover

Problem

When Claude takeover is already active, updating Claude common config can persist the snippet in cc-switch while leaving the active live config stale.

In practice this means fields like statusLine (or simpler env keys) can exist in Claude common config but never appear in ~/.claude/settings.json until some later operation rewrites live config.

Root cause addressed here

The takeover-active post-commit path used ProxyLiveBackup and saved a refreshed backup snapshot, but it did not refresh the active Claude live config. It also rebuilt backup state from the stored common snippet instead of the in-flight snippet being applied by the current operation.

This patch:

1. passes the current common-config snippet through the takeover backup snapshot path
2. refreshes active Claude live config after saving the takeover backup snapshot

Verification

Already verified locally before preparing this PR:

• cargo build --lib
• targeted integration test for the new regression case
• takeover + common_config related test selection
• full lib test suite
• full provider_commands integration tests

Regression coverage

Added:

• updating_claude_common_config_under_takeover_refreshes_active_live_settings

Issue

Closes #338