[ajaykr0905]

Summary

 health initialization
-  every backend waits for Redis readiness
+  Redis waits for a confirmed connection
+  memcache treats the nonexistent Redis dependency as ready

• keep Redis startup health behavior unchanged
• let memcache-backed servers report healthy without constructing a Redis client
• cover the configured server's public HTTP health-check response

Fixes #1284.

Evidence

• Before: go test ./test/server -run '^TestMemcacheServerStartsHealthy$' -count=1 failed with expected: 200, actual: 500.
  After: the regression passed 10 consecutive runs and go test -race ./test/server -count=1 passed.
• make tests_unit
• make check_format
• go vet ./...
• pre-commit run -a

Merge Danger

Door: Two-way

The change is isolated to initial health state and can be reverted without data migration or configuration changes.

Blast Radius: Readiness

Only BACKEND_TYPE=memcache startup health changes; Redis continues to start unhealthy until its connection is confirmed, and config readiness remains independently enforced.

Assisted-by: OpenAI Codex