fix(app): use project server for prompt drafts

[Brendonovich]

Summary

• promote new-session drafts with the server associated with the selected project
• remove the active-server dependency from prompt submission
• add regression coverage for drafts whose project server differs from the active server

Testing

• bun test src/components/prompt-input/submit.test.ts (from packages/app)
• bun typecheck (from packages/app)
• pre-push bun turbo typecheck (29 tasks passed)