travis, build: speed up CI runs (#17854)

* travis: exclude non-test jobs for PRs

We don't usually look at these builders and not starting them
removes ~15min of build time.

* build: don't run vet before tests

Recent versions of Go run vet during 'go test' and we have
a dedicated lint job.

* build: use -timeout 5m for tests

Tests sometimes hang on Travis. CI runs are aborted after 10min with no
output. Adding the timeout means we get to see the stack trace for
timeouts.