Raise the go test timeout so internal/handlers fits

With the two races fixed, internal/handlers still hit the 30s
-timeout in the Docker build. Its time is real work, not clock
waits: each test starts its own server and in-memory database, and
each new session writes its welcome lines to the database one row at
a time, which the race detector slows down. The only clock waits are
the one-second long poll and a 200ms pause.

Measured in docker build --no-cache .: internal/handlers took 21-30s
under -race, and over 30s in the review builds that timed out.

Both go test runs in the test target now use -timeout 120s. The
retry stays (#101).

Model: opus-5-5

Makefile

@@ -32,7 +32,7 @@ fmt-check:
 	@test -z "$$(gofmt -l .)" || (echo "Files not formatted:" && gofmt -l . && exit 1)
 
 test: ensure-web-dist
-	go test -timeout 30s -race -cover ./... || go test -timeout 30s -race -v ./...
+	go test -timeout 120s -race -cover ./... || go test -timeout 120s -race -v ./...
 
 # check runs all validation without making changes
 # Used by CI and Docker build — fails if anything is wrong