I have both 2.9 and 2.83 on the same laptop. 2.83 shows all the appropriate options for Cycles in both the Properties panel and the Preferences/System panel, but 2.9 doesn’t have any references to Cycles in either. Same machine.
Solved it: to my surprise, CYCLES is an add-on (!!!) , and must be installed like any other addon. It does, of course, come with the standard download.
It’s weird. In that case it was either another bug or @Jeric_Synergy accidentally disabled Cycles at some point. Or maybe some new addon disabled Cycles? I’m not sure if an addon is allowed to do that (in terms of Blender security/safety)