[ENHANCEMENT] Extract ChatView ask/footer state for approval-flow work

[roomote]

Problem (one or two sentences)

The ask/footer state logic in ChatView is bundled into a large effect, which makes approval-related behavior harder to review and change safely. That increases the cost of fixing the approval-control flash.

Context (who is affected and when)

This affects contributors working in the chat UI, especially when touching approval, footer buttons, or ask-state behavior. It matters now because issue #102 needs small, reviewable changes in this area.

Desired behavior (conceptual, not technical)

The chat UI should have a small, easy-to-read unit responsible for deriving ask/footer state so behavior changes are easier to review and test.

Constraints / preferences (optional)

Match existing repo patterns by extracting a focused hook/helper. Do not introduce a new reducer or state-machine abstraction for this area.

Request checklist

• I've searched existing Issues and Discussions for duplicates
• This describes a specific problem with clear context and impact

Zoo Code Task Links (optional)

• https://app.roomote.dev/task/2t7u9db2gc882

Acceptance criteria (optional)

• The lastMessage -> ask/footer-state derivation in ChatView is extracted into a focused hook/helper.
• There is no intended behavior change.
• Existing ask flows covered by ChatView tests continue to behave the same.
• The change is small enough to review independently as a 1 SP prep step for [ENHANCEMENT] Reduce approval-control flash for auto-approved read-only asks #102.

Proposed approach (optional)

Extract the logic currently living around the ask/footer-state branch in ChatView into a useAskUiState-style hook/helper, similar in spirit to other focused webview hooks already used in this repo.

Trade-offs / risks (optional)

This is prep work, so the main risk is over-abstracting. Keep the extraction narrow and behavior-preserving.