Switch backend port from 5000 to 5057

Port 5000 caused recurring collisions with stray processes across subagent
runs. 5057 is uncontested in this environment. CORS unaffected (Vite dev
origin is 5173).

backend/Properties/launchSettings.json

@@ -4,7 +4,7 @@
     "backend": {
       "commandName": "Project",
       "launchBrowser": false,
-      "applicationUrl": "http://localhost:5000",
+      "applicationUrl": "http://localhost:5057",
       "environmentVariables": {
         "ASPNETCORE_ENVIRONMENT": "Development"
       }

docs/superpowers/plans/2026-08-15-supabase-todo-app.md

@@ -157,7 +157,7 @@ From the repo root:
 dotnet new webapi --name backend --framework net9.0 --no-https --use-controllers --output backend
 ```
 
-`--no-https` keeps local dev on plain `http://localhost:5000` (matches CORS config in Task 7). `--use-controllers` gives us `Controllers/`-based routing instead of minimal APIs.
+`--no-https` keeps local dev on plain `http://localhost:5057` (matches CORS config in Task 7). `--use-controllers` gives us `Controllers/`-based routing instead of minimal APIs.
 
 Delete the sample files the template generates:
 
@@ -187,7 +187,7 @@ Replace `backend/Properties/launchSettings.json` with:
     "backend": {
       "commandName": "Project",
       "launchBrowser": false,
-      "applicationUrl": "http://localhost:5000",
+      "applicationUrl": "http://localhost:5057",
       "environmentVariables": {
         "ASPNETCORE_ENVIRONMENT": "Development"
       }
@@ -264,7 +264,7 @@ cd backend
 dotnet build
 dotnet run &
 sleep 3
-curl -s -o /dev/null -w "%{http_code}\n" http://localhost:5000/openapi/v1.json  # 200 if webapi template's OpenAPI is on
+curl -s -o /dev/null -w "%{http_code}\n" http://localhost:5057/openapi/v1.json  # 200 if webapi template's OpenAPI is on
 kill %1
 ```
 
@@ -685,7 +685,7 @@ sleep 5
 - [ ] **Step 2: Confirm unauthenticated requests are rejected**
 
 ```bash
-curl -s -o /dev/null -w "%{http_code}\n" http://localhost:5000/api/todos
+curl -s -o /dev/null -w "%{http_code}\n" http://localhost:5057/api/todos
 ```
 
 Expected: `401`.
@@ -716,7 +716,7 @@ If `TOKEN` length is under 100 chars, sign-up did NOT return a session — email
 - [ ] **Step 4: GET (empty list)**
 
 ```bash
-curl -s -w "\nHTTP %{http_code}\n" -H "Authorization: Bearer $TOKEN" http://localhost:5000/api/todos
+curl -s -w "\nHTTP %{http_code}\n" -H "Authorization: Bearer $TOKEN" http://localhost:5057/api/todos
 ```
 
 Expected: `[]` then `HTTP 200`.
@@ -724,7 +724,7 @@ Expected: `[]` then `HTTP 200`.
 - [ ] **Step 5: POST (create)**
 
 ```bash
-curl -s -w "\nHTTP %{http_code}\n" -X POST http://localhost:5000/api/todos \
+curl -s -w "\nHTTP %{http_code}\n" -X POST http://localhost:5057/api/todos \
   -H "Authorization: Bearer $TOKEN" -H "Content-Type: application/json" \
   -d '{"title":"buy milk"}'
 ```
@@ -735,7 +735,7 @@ Expected: a JSON body with `id`, `title:"buy milk"`, `completed:false`, `created
 
 ```bash
 TID=<id from previous step>
-curl -s -w "\nHTTP %{http_code}\n" -X PATCH "http://localhost:5000/api/todos/$TID" \
+curl -s -w "\nHTTP %{http_code}\n" -X PATCH "http://localhost:5057/api/todos/$TID" \
   -H "Authorization: Bearer $TOKEN" -H "Content-Type: application/json" \
   -d '{"completed":true}'
 ```
@@ -745,7 +745,7 @@ Expected: JSON with `completed:true`, `HTTP 200`.
 - [ ] **Step 7: DELETE**
 
 ```bash
-curl -s -w "\nHTTP %{http_code}\n" -X DELETE "http://localhost:5000/api/todos/$TID" \
+curl -s -w "\nHTTP %{http_code}\n" -X DELETE "http://localhost:5057/api/todos/$TID" \
   -H "Authorization: Bearer $TOKEN"
 ```
 
@@ -829,7 +829,7 @@ Create `frontend/.env.example`:
 ```
 VITE_SUPABASE_URL=https://YOURPROJECT.supabase.co
 VITE_SUPABASE_PUBLISHABLE_KEY=sb_publishable_YOURKEY
-VITE_API_URL=http://localhost:5000
+VITE_API_URL=http://localhost:5057
 ```
 
 - [ ] **Step 2: Create `frontend/.env.local` with real values**
@@ -837,7 +837,7 @@ VITE_API_URL=http://localhost:5000
 ```
 VITE_SUPABASE_URL=https://jrbqfctqhjttxobtoqts.supabase.co
 VITE_SUPABASE_PUBLISHABLE_KEY=sb_publishable_QajbbpfedzxWEhCPBKTZqg_M-8qyCUy
-VITE_API_URL=http://localhost:5000
+VITE_API_URL=http://localhost:5057
 ```
 
 - [ ] **Step 3: Create the Supabase client module**
@@ -1351,7 +1351,7 @@ cd backend && dotnet run
 cd frontend && npm run dev
 ```
 
-Expected: backend on `http://localhost:5000`, Vite on `http://localhost:5173`.
+Expected: backend on `http://localhost:5057`, Vite on `http://localhost:5173`.
 
 - [ ] **Step 2: Sign up**
 
@@ -1450,7 +1450,7 @@ Two terminals:
 
 ```bash
 # Terminal 1
-cd backend && dotnet run          # http://localhost:5000
+cd backend && dotnet run          # http://localhost:5057
 
 # Terminal 2
 cd frontend && npm run dev        # http://localhost:5173