[Feat] Add side chats alongside active Sessions

[roomote-roomote]

​Opened on behalf of @daniel-lxs. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

What changed

• adds a per-person side conversation linked to its parent Session rather than modeling discussion as another coding task
• opens side chat in the existing responsive workspace: beside the main Session on desktop and as the selected panel on mobile
• gives side chat the initiating user's normal Fast capabilities while keeping its transcript distinct from the parent conversation
• keeps side chats out of top-level Session lists and prevents nesting side chats beneath side chats

Why this change was made

People need a place to interrogate, challenge, and discuss ongoing work without mixing that discussion into the main task conversation. A linked Fast Session reuses the existing conversation, authorization, and integration model without weakening task ownership or reply routing.

Impact

Session viewers can open an action-capable side chat from the workspace rail and continue using normal Roomote tools there. The main Session and coding task continue independently, while the side-chat relationship remains explicit in storage.

[roomote-community]

No new code issues found. See task

_{Reviewed fa69c5f}

[roomote-roomote]

Resolved the CI regressions and merge conflict on fa69c5f. Latest develop already carried the repository-less-environment fixture correction, so the conflict kept its clearer missing-name fixture. The remaining PR-specific failure came from sessions/index.test.ts evaluating the new Fast-session reader through an incomplete DB mock; the test now mocks that dependency at its module boundary. The affected 19 web server tests, 14 declarative-environment tests, 2 side-chat persistence tests, 53 responsive workspace tests, repo-wide fast typecheck, and pre-push lint/typecheck/knip checks pass. GitHub’s replacement Test job and all other required CI checks pass. This fixer cycle’s visual-proof step timed out, so PR proof embeds were removed rather than presenting stale evidence as current.