Revamp mobile sidebar project/session experience

[ronak-guliani]

What does this PR do?

The mobile sidebar was still using the old mixed project/session layout and did not support smooth project switching from the app. This revamps packages/mobile with clear flat Projects and Sessions sections, per-project new-session actions, and folder-path add/search so new projects can be added directly from mobile. It updates connection/client/store flow to support project list refresh, project switching, state resets, and event stream restart when switching contexts. It also fixes sidebar drawer/background color behavior for light and dark mode by removing transparent drawer rendering and using consistent theme surfaces.

How did you verify your code works?

• bun run typecheck (from packages/mobile)

[github-actions]

Hey! Your PR title Revamp mobile sidebar project/session experience doesn't follow conventional commit format.

Please update it to start with one of:

• feat: or feat(scope): new feature
• fix: or fix(scope): bug fix
• docs: or docs(scope): documentation changes
• chore: or chore(scope): maintenance tasks
• refactor: or refactor(scope): code refactoring
• test: or test(scope): adding or updating tests

Where scope is the package name (e.g., app, desktop, opencode).

See CONTRIBUTING.md for details.