build: remove defunct test-postgres rule (#22839)

The `test-postgres` Makefile rule was redundant — CI never used it (it
runs `test-postgres-docker` + `make test` via the `test-go-pg` action),
and `make test` auto-starts a Postgres Docker container when needed via
`dbtestutil`.

- Remove the `test-postgres` rule from Makefile
- Update `pre-push` to run `test-postgres-docker` in the first phase
(alongside gen/fmt) and `make test` in the second phase
- Fix stale comments in CI workflows referencing `make test-postgres`
- Remove redundant "Test Postgres" entries from docs since `make test`
handles Postgres automatically

.claude/docs/DATABASE.md

@@ -189,8 +189,8 @@ func (q *sqlQuerier) UpdateUser(ctx context.Context, arg UpdateUserParams) (User
 ### Common Debug Commands
 
 ```bash
-# Check database connection
-make test-postgres
+# Run tests (starts Postgres automatically if needed)
+make test
 
 # Run specific database tests
 go test ./coderd/database/... -run TestSpecificFunction

.claude/docs/TESTING.md

@@ -67,7 +67,6 @@ coderd/
 | `make test` | Run all Go tests |
 | `make test RUN=TestFunctionName` | Run specific test |
 | `go test -v ./path/to/package -run TestFunctionName` | Run test with verbose output |
-| `make test-postgres` | Run tests with Postgres database |
 | `make test-race` | Run tests with Go race detector |
 | `make test-e2e` | Run end-to-end tests |
 

.claude/docs/WORKFLOWS.md

@@ -109,7 +109,6 @@
 
 - Run full test suite: `make test`
 - Run specific test: `make test RUN=TestFunctionName`
-- Run with Postgres: `make test-postgres`
 - Run with race detector: `make test-race`
 - Run end-to-end tests: `make test-e2e`