Add readiness probes for web-app and website dev servers

[pcarrier]

Summary

• Adds HTTP readiness probes for web-app (Vite, port 3265) and website (Astro, port 4321) in process-compose.yml.

Motivation
Follow-up to #136. Without readiness probes, dev-check considers these services ready as soon as pnpm install starts running. Now all five services have readiness probes, so dev-check waits for every dev server to actually be serving before proceeding.

Testing
Covered by the dev-check CI job.

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[indent]

PR Summary

This PR adds HTTP readiness probes for the web-app and website dev servers in process-compose.yml, so that dependent services wait for the servers to actually be serving (Vite on port 3265, Astro on port 4321) before proceeding, rather than considering them ready as soon as pnpm install starts.

• Added readiness_probe with http_get to web-app (port 3265) and website (port 4321), matching the existing gateway probe pattern
• Both probes use the same timing parameters as other services: 5s initial delay, 2s poll interval, 300 failure threshold (~10 min timeout)

Issues

No issues found.

CI Checks

All CI checks pass on the latest commit (0e8d37e). The --host flag added to the Astro dev command resolved the previous dev-check timeout.

[github-actions]

Coverage

Crate	Lines	Functions	Regions
alacritty-driver	59.7% (529/886)	62.5% (40/64)	59.8% (754/1261)
browser	0.0% (0/807)	0.0% (0/65)	0.0% (0/1370)
cli	43.8% (1426/3256)	59.6% (190/319)	49.4% (2514/5088)
fonts	76.9% (486/632)	85.5% (47/55)	78.2% (922/1179)
gateway	35.2% (242/688)	32.4% (23/71)	26.9% (293/1088)
remote	83.0% (1900/2290)	91.1% (184/202)	85.8% (3612/4212)
server	43.7% (1548/3544)	58.3% (176/302)	44.1% (2606/5906)
webrtc-forwarder	0.0% (0/1464)	0.0% (0/93)	0.0% (0/2501)
webserver	59.3% (233/393)	75.9% (44/58)	64.8% (455/702)
Total	45.6% (6364/13960)	57.3% (704/1229)	47.9% (11156/23307)