Customizations migration: Hint disappears or reappears unexpectedly through reloads, settings changes

Testing #334500

- Set the settings from the TPI
- At this point, I have `chat.customizations.migrationHint` set to `always`
- Clone and open https://github.com/aeschli/vscode-customization-migration-test in Insiders
- Send a couple messages to the Copilot harness running in the Agent Host
- I get the migration hint in the chat panel
- Reload VS Code
- ❓ The migration hints are now missing from the chat panel
- Set `chat.customizations.migrationHint` to `once`, reload VS Code, start a new chat, get hint once (as expected)
- Reload VS Code
- ❓ Migration hint disappears again from existing session
- I send another message in existing session and ❓ get the migration hint again while the agent is working (even though `chat.customizations.migrationHint` is set to `once`, and I had gotten the hint before reload).
- But maybe this is expected, since the hint is now missing after a reload?
- But after the agent finishes its work, the hint disappears (no reload required for it to disappear this time)
- Send additional messages in the same chat, and ❓ now I get the migration hint each time (even though `chat.customizations.migrationHint` is still set to `once`)
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