Add docs CTAs, sticky install banner, and analytics tracking

[AvdLee]

Motivation

• Increase install conversions from docs traffic with low-risk, additive UX patterns while preserving the existing design system and performance.
• Provide lightweight instrumentation to measure CTA impressions, clicks, and banner interactions using the existing Plausible integration when available.

Description

• Added a reusable DocsCTA Astro component supporting title, description, primary, optional secondary, a compact variant, responsive layout, accessible focus states, and data attributes for analytics hooks.
• Added a dismissible, mobile-friendly DocsInstallBanner component that persists dismissal in localStorage and is dark-mode compatible.
• Integrated automatic placement by rendering hidden CTA templates and the banner from src/components/starlight/Footer.astro and injecting them into docs pages via a small client script src/scripts/docs-engagement.ts (inserts a compact CTA after the first major content section and a full CTA at the bottom) without modifying MD/MDX sources.
• Instrumented events to use the existing Plausible helper when available, tracking Docs CTA Impression (with placement), CTA clicks (per-CTA event names), Docs Banner Shown, Docs Banner Dismissed, and Docs Banner Click.
• Added scoped styling in src/styles/starlight-custom.css to match the Starlight design tokens and provide accessible focus outlines and responsive behavior.
• Files changed / components added / integration points: modified src/components/starlight/Footer.astro and src/styles/starlight-custom.css, added src/components/starlight/DocsCTA.astro, src/components/starlight/DocsInstallBanner.astro, and src/scripts/docs-engagement.ts, and wired the client module into the docs footer to run only on docs content pages.

Testing

• Ran cd docs && npm run lint and lint passed successfully.
• Ran cd docs && npm run format:check (Prettier) and formatting passed successfully after adjustments.
• Ran cd docs && npm run typecheck and type checks passed (client script compiled as a module and exported an empty export to satisfy module scope).
• Ran cd docs && npm run knip and it completed successfully.
• Ran cd docs && npm run build which completed client and static build steps locally but the full build failed in this environment due to an external network fetch error in src/pages/blog/[slug].astro (ENETUNREACH), unrelated to the CTA/banner changes; the docs-specific changes themselves did not trigger errors.

TODO / Recommendations

• Optionally align CTA event naming with existing plausible-event-name=... taxonomy for easier dashboard grouping.
• Consider excluding the docs homepage from the automatic insertions if overlapping homepage CTAs are undesirable (see src/components/starlight/PageTitle.astro).
• Monitor metrics after rollout and A/B test messaging or placement if desired.

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Codex Task

[AvdLee]

Closing this, we will do it differently