//Hi, I'm having a bug where the number of gem cutting shapes available went down one by one until I have none available now (and I can only "give gift" with uncut gems).// (apparently strikethrough styling doesn't work) Never mind that, I think the actual issue is that I didn't have enough money for the nicer cuts so they just didn't appear in the list instead of being greyed out and telling me why they were. But anyway, cheating gem cutting still would be useful still.
It seems to be a household-wide setting and not a sim-specific thing, and also I didn't find any trance of gem-cutting skill, neither online nor in the skill list available from mastercontroller/advanced/skill.
Where, in the MasterController options (or otherwise for that matter), might I find the option to reset/change my sim's (household's) gem-cutting "skill" ?

There isn't an option to do so because I don't believe it exists as a skill, hidden or otherwise. If anything, it's most likely tied to the Collection Journal simply as a stored number.
There's a mod on MTS called More Gem Cutting Options, which has packages for permanently unlocking all the cuts if you would prefer.