OPS-1: Dockerfiles (net10 API + nginx frontend) + production config

- GerbilManagerWebAPI/Dockerfile: net7->net10 multi-stage; build context=repo
  root (includes ServiceDefaults); port 8080 (.NET 10 container default)
- gerbil-manager-web/Dockerfile: drop VITE_API_BASE_URL build-arg; nginx proxies
  /api/* to api:8080 (strip prefix), /scalar, /openapi/ -- one published port 80
- gerbil-manager-web/src/api/client.ts: default API_BASE_URL /api (relative),
  no hostname coupling at build time; Aspire still injects absolute LAN URL in dev
- GerbilManagerWebAPI/Program.cs: run EF Migrate() at startup always (not Dev-only)
- GerbilManager.ServiceDefaults/Extensions.cs: expose /health + /alive in all
  environments (compose healthcheck requires them in Production)

Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>

gerbil-manager-web/src/api/client.ts

@@ -2,11 +2,12 @@ import { de } from '../strings/de'
 
 /**
  * Basis-URL der GerbilManagerWebAPI.
- * Per VITE_API_BASE_URL konfigurierbar (z. B. in Docker / Aspire);
- * Standard ist das lokale Dev-Profil der API (launchSettings.json, Profil "http").
+ * Dev (Aspire): VITE_API_BASE_URL wird von AppHost zur Laufzeit gesetzt (LAN-IP + Port).
+ * Produktion (Docker/nginx): kein Env-Var nötig — nginx proxyt /api/* zum API-Container,
+ * daher funktioniert der relative Pfad /api auf jedem Host ohne Build-Zeit-Kopplung.
  */
 export const API_BASE_URL: string =
-  import.meta.env.VITE_API_BASE_URL ?? 'http://localhost:5179'
+  import.meta.env.VITE_API_BASE_URL ?? '/api'
 
 export class ApiError extends Error {
   readonly status: number | null