[Task] Replace middle-dot (·) separators with gap, per the DESIGN.md no-dot rule

[Astro-Han]

Goal

No · middle-dot separators remain in PawWork product-UI chrome, per the DESIGN.md "Do's and Don'ts" rule (separate with gap + typographic contrast). Any · that genuinely reads best in a dense metadata row is instead registered as a sanctioned exception in DESIGN.md, not left as silent drift.

Scope

In scope — the four call sites that render a literal · in user-facing chrome:

• packages/ui/src/components/message-part/user-message.tsx:72 and :165 — user-bubble bottom toolbar joins model name and time with ·.
• packages/ui/src/components/assistant-turn-footer.tsx:52 — agent-round footer joins agent / model / duration / interrupted with ·.
• packages/ui/src/components/rate-limit-card.tsx:85 (with rate-limit-card.css __sep) — rate-limit card headline separates title and reset time with ·.
• packages/app/src/components/prompt-input/context-items.tsx:44 — file-context tooltip puts · between the label and the path.

For each site: replace · with gap + typographic contrast (the canonical fix), or register it as a DESIGN.md exception (id + rule broken + reason) if a dot is genuinely warranted there.

Out of scope — any other separator/spacing redesign; · inside code comments (e.g. rate-limit-card.css:6) and docs prose, which are not product UI.

Relevant files or context

DESIGN.md rule (Do's and Don'ts): "The middle-dot · as a separator or decoration in product UI — separate with gap plus typographic contrast (sans vs mono, alphanumeric vs colon-time)."

Surfaced during the DESIGN.md condensation: the no-· rule was deliberately kept, so these pre-existing violations were not silently legitimized. The same pass found the · join helper duplicated across the two timeline footers (user-message.tsx / assistant-turn-footer.tsx), so a shared gap-based meta-row helper may be the cleanest fix for those two.

Verification

• grep -rn "·" packages/app/src packages/ui/src over .tsx/.css returns no hits in product-UI render paths (comments/docs excluded), or each remaining hit maps to a registered DESIGN.md exception.
• Visually confirm the affected surfaces (user-bubble toolbar, agent footer, rate-limit card, context tooltip) still read clearly with gap-based separation — bun run dev:desktop walk, or a snap of the relevant target.

Execution mode

Investigate and propose a plan first — post the per-site decision (gap fix vs registered exception) as an issue comment and wait for an explicit "approved" before writing code or opening a PR.

[Astro-Han]

Two of the four sites are now done in #1211 (commit 8702603), by request, as part of reworking the conversation footer meta row:

• user-message.tsx and assistant-turn-footer.tsx — the agent · model · time join and the inter-token separator spans are replaced by a flex gap; the user-message timestamp renders in mono + tabular-nums for the sans-vs-colon-time contrast the rule calls for. (The shared gap-meta helper this issue floated was not extracted: the two footers differ enough structurally that inline gap rules were simpler than a shared abstraction. The dead agent label was dropped at the same time.)

Remaining scope for this issue, unchanged, still via the propose-first flow:

• rate-limit-card.tsx (+ rate-limit-card.css __sep)
• context-items.tsx

A · grep over the two timeline footers now returns no product-UI hits.