IMHO, the Shillelagh cantrip should work with Greatclub as D&D 2024 Druids have simple weapon proficiency, which includes Greatclubs. By the rules as written, it is more ambiguous. I haven't found any Sage Advice specifying either way.
I would be somewhat hesitant as a DM to allow Shillelagh to be extended to other items. My criteria would be is it a wooden bludgeoning simple melee weapon? Club, greatclub, and quarterstaff qualify on those grounds. A wooden mace also qualifies. This seems reasonable if you look at the style of the weapons on page 216 of the 2024 Player's Handbook, a Mace looks quite similar to a club with a slightly different head on it.
With those criteria, I would not allow a musket or rifle to benefit from the Shillelagh cantrip. However, mechanically when used in melee, it would not be unbalanced to allow it to benefit from Shillelagh. Sometimes in D&D we get too strict about what a character can do within the rules as written. If the concept is not unreasonable and not unbalanced, it can be more fun to play with a "Yes, you can" approach.