Setting the TIMEOUT environment variable has been a noop in both cases since its introduction.
It seems to have been inadvertently copy-pasted from existed code. For example, in commit d80e3cbece857b293a4903ef49c4d543bb2cfb7f, it was needlessly copied from a valid case a few lines above for the qa/pull-tester/run-bitcoind-for-test.sh script.