Create a PHPUnit group in mediawiki/core, add a new testsuite that would exclude the group in gated runs and then switch the wmf-quibble jobs to use that new suite.
Background
Several extensions[1] that should be added to the extension-gated CI runs have very time consuming tests that would increase run time tremendously. Therefore these extensions are not added to the gated runs, potentially risking that things break unnoticed.
See also the discussion roughly starting here T125050#5120646
[1] Scribunto, CirrusSearch or the FileImporter from Move-Files-To-Commons