[Feat] Add homepage feedback prompt

[roomote-roomote]

Created by Roomote. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

What changed

• Added a compact feedback prompt beside the homepage bottom-sheet tabs.
• Added a feedback dialog with options to book time with the founders or send feedback by email.
• Persisted prompt dismissal locally so it stays hidden on future visits.
• Added focused coverage for the dialog actions and dismissal behavior.

Why this change was made

The homepage now offers a lightweight, contextual way for users to share feedback without interrupting their normal workflow.

Impact

Users can open the feedback options directly from the homepage or dismiss the prompt permanently in their current browser.

Screenshots

[roomote-community]

No new code issues found. See task

• apps/web/src/app/(authenticated)/home/Home.tsx:82-96 — Guard storage reads and writes. Storage failures now keep the prompt usable for the current session.

_{Reviewed 55d024c}