Github MCP app forgets state across session open

[connor4312]

From microsoft/vscode#327808

3. Start a session which ends up using the Github mcp app for creating the PR
4. Press Create pull request
5. MCP collapses into a reference to the PR
6. open a different session
7. go back to the initial session
8. 🐛 MCP app shows create pull request form again

[cipheraxat]

Working on a fix in #2971