fix(board): scope projects to selected familiar

[CompleteDotTech]

Summary

• scope Board inspector projects to an already-selected familiar
• scope New Task project choices when a familiar is preselected
• retain an authorized familiar when choosing one of its accessible projects, while clearing a potentially stale linked session

Why

PR #3707 fixed the Project -> Familiar direction from #3703. Familiar-first task flows still showed the global project list, which could invite a pairing that later failed session-launch authorization. This applies the same server-side access scope in the inverse direction.

Validation

• typecheck
• test wiring
• app suite (892 files)
• focused New Task and Board project-picker tests