fix(chat): render avatar progress badge that was invisible

[dvargasfuertes]

Fixes the avatar progress badge reporting visible: true via the debug API while never painting on screen, by passing isProcessing to the empty-state avatar and making the badge dot lay out at its real size. This restores the only visual signal that the assistant is processing once the useProgressBadge flag is on.

Root cause analysis

(a) How did the code get into this state? The progress-badge feature (#32680) wired isProcessing into the transcript ChatAvatar but not the empty-state one, so the empty-state badge was never created. Separately, it reused BusyIndicator for the badge dot. BusyIndicator is a bare <span>, which defaults to display: inline — and width/height do not apply to non-replaced inline elements. Its only prior caller wrapped it in a flex parent, where flex items are blockified, so the inline default never mattered. Inside the new non-flex ProgressBadge wrapper the dot stayed inline and collapsed to 0×0, so even when the badge mounted it painted nothing.

(b) What mistakes or decisions led to it? Two parallel render paths (empty-state vs transcript) were kept in sync by hand, so one was missed. And a primitive whose sizing silently depended on its parent's layout context was reused in a new context without that dependency.

(c) Were there warning signs we missed? The debug API deliberately reports the same isProcessing && isProgressBadgeEnabled() gate the component uses, so it reported visible: true — which masked the fact that the DOM node had no size. There was no test asserting the dot actually has dimensions.

(d) What can we do to prevent recurrence? A self-contained visual primitive shouldn't depend on its parent's display to size itself. BusyIndicator is now inline-block so it lays out at its declared size anywhere, and a regression test asserts that.

(e) AGENTS.md change? Not warranted. This is a narrow CSS-layout gotcha, not a project-wide rule; encoding "inline spans ignore width/height" as a durable rule would add noise that goes stale. The regression test is the right guard.

Test plan

• bunx tsc --noEmit and bun run lint pass.
• New busy-indicator.test.tsx asserts the dot is block-level and sized; existing three-dot-indicator and tool-call-chip suites still pass (the chip already wraps the dot in a flex parent, so its rendering is unchanged).
• Reproduced locally via Playwright/CDP against the empty-state avatar with the useProgressBadge flag on: before, the badge span was absent / its dot measured 0×0 (display: inline); after, the dot measures ~6×6 (display: inline-block) and the pulsing badge is visible in the avatar's bottom-right.

Link to Devin session: https://app.devin.ai/sessions/4ecf21400f764b59ad1eecabd1535956
Requested by: @dvargas92495

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