fix(max): constrain chat composer height

[lordspline]

Problem

People who paste long prompts into PostHog AI can lose the send controls below the viewport on compact screens.

Closes PostHog#62461

Changes

• The textarea now caps its height responsively and scrolls long prompt content internally.
• The composer stays within the viewport while queued messages scroll before displacing the input controls.
• Short prompts retain their existing auto-growth behavior.

Viewport	Textarea bottom	Send control bottom	Result
390 × 500 before	497 px	529 px	Send control clipped
390 × 500 after	440 px	472 px	Both controls visible
390 × 844 after	570 px	602 px	Both controls visible
1366 × 768 after	527 px	559 px	Both controls visible
1440 × 900 after	593 px	625 px	Both controls visible
1440 × 900 panel after	657 px	689 px	Both controls visible

Screenshots and a short demo are attached to the Capy handoff. This contributor account cannot publish to PostHog/pr-assets.

How did you test this code?

• Focused Jest coverage catches composer overflow, Enter and Shift+Enter behavior, and disabled states.
• Browser QA covered the main scene, sidebar panel, laptop, narrow, and compact narrow viewports.
• Browser QA covered paste, internal scrolling, submission, autocomplete positioning, loading controls, and hands-free controls.
• The frontend type check and hogli ci:preflight --fix pass locally.

Automatic notifications

• Publish to changelog?

Docs update

None. This fixes existing composer layout behavior.

🤖 Agent context

Autonomy: Human-driven (agent-assisted)

Capy implemented and browser-tested this change. It used /writing-ui-components, /writing-tests, /qa-frontend, /running-ci-preflight, and /writing-pr-descriptions.

The test prompt and visual evidence use invented local data.

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