#22833 fix(webviews): composer and background-task browser tests pass on base again (react-apps-check red)

Summary

cmux-next web / react-apps-check (1–4) has been red on feat-cmux-next pushes since #22741 and #22667 landed together, and since #22636. Each shard fails one file (base run 39530699937, 6c256dfb9a):

Shard	File	Cause
1	composer-row-rhythm.test.ts	timeout waiting for .acpmux-steer-now
3	composer-turn-cycle.test.ts	timeout waiting for .acpmux-steer-now
4	composer-draft-wrap.test.ts	timeout (file limit 120 s)
2	agent-pane-background-tasks.test.ts	title expected "Show output", got null

• Steer control: #22741 draws ↵ only for an agent that reports acpmux steering. The composer-row and turn-cycle gallery fixtures are Claude Code chats but never set it, so ↵ never appeared. Both now set steering: true.
• Gap: with ↵ drawn in #22667's plain footer, Stop follows it and both add an inset, giving steer→Stop 16 px against Stop→mic 10 px. ↵ now drops its trailing inset when Stop follows it (composerLocation.css), so the three draw one gap apart. This is what the rhythm test checks.
• Background task: #22636 removed the note's "Show output" tooltip for tooltip-rules. The test still asserted it; that line goes, and the click-opens-terminal check stays.

Testing

With CMUX_BROWSER_TESTS=1 on huge-blue (Linux, Chromium):

• bun test test/composer-row-rhythm.test.ts: base, 0 pass / 8 fail (.acpmux-steer-now timeout; with the fixture alone, uneven gaps inside groups: steer→send 16.0, send→mic 10.0). Head: 8 pass.
• bun test test/agent-pane-background-tasks.test.ts test/composer-turn-cycle.test.ts: base, background-tasks 1 fail and turn-cycle 3 fail (steer timeouts). Head: background-tasks passes (4/4); turn-cycle not yet seen green (see below).
• scripts/web-lint.sh: passes.

Observed / Not run

• Observed: the runs above.
• Not seen green locally: composer-turn-cycle and composer-draft-wrap on head. The box was at load ~100 and Vite's 100 s warm-up timed out before any test ran. The react-apps-check shards on this PR are the evidence for those.

Changelog

none

Agent session: huge-blue

🤖 Generated with Claude Code

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Summary by cubic

Fixes the react-apps-check browser-test shards that were red on feat-cmux-next: the composer gallery fixtures never reported acpmux steering, so the ↵ control was never drawn and the rhythm/turn-cycle tests timed out, and the background-task test still read a "Show output" tooltip that no longer exists.

• The composer-row and turn-cycle fixtures now set steering: true; both are Claude Code chats, which steer.
• ↵ drops its trailing inset when Stop follows it, so steer, Stop, and mic sit one gap apart.
• The background-task test no longer asserts the removed "Show output" tooltip; the click-opens-terminal check stays.