Gonna add a +1 for basically any type of grease that's adorable for bearings or shafts. The key is going to be making sure you don't goober it on there.
Synthetic helps in winter, especially with tighter tolerances.
As for frog lube.... There are actually some low strain/low pressure applications where it works well. For example, the gas valve on my weatherby semi auto 12 gauge. Warm up the mag tube, and use a paper towel to smear it on. Watch it melt, then heat up the tube again, and wipe it off after it cools and hardens again. All that's left is a very thin coating you can't see, but can feel. I do the same to the valve itself. Throw it on and it works beautiful, to clean it you just do the same procedure with a wipe beforehand.
But that's an incredibly low stress application. I tried it on bolt carriers etc and I didn't like it. It provided no real protective layer or barrier. It also doesn't really clean very well. It rarely gets used anymore now that break free clp is on the shelf, along with various types of grease (no they aren't allocation specific, I just have a few syringes full because I thought I lost one, filled a new one, then found the first, lather rinse repeat)