Dormant figs don't need much moisture over the winter. Even my smaller figs will usually be fine until spring without additional water if they go into the garage well watered. You don't say how big your fig's pot is, or how much water you added every 6-8 weeks. But from your description, it sounds as if it might have rotted from the bottom up. You could pull it out of the pot and check the roots for rot.

Over the winter, it was in a 6" pot, and I probably added about a half cup of water every 6-8 weeks. I've since transplanted it to a 12" or so pot, and the roots seemed alright (if a little rootbound).

Younger figs are more vulnerable than older figs, but that amount of water doesn't seem likely to have caused a problem.

Was the fig heavily wrapped while in the garage? There have been reports of delayed leafing out in that instance. Or if the garage has been cold, perhaps it just isn't ready to grow yet.

In any case it won't hurt to give it more time. Good luck.

The coming back to life depends on how cold it got in the garage during the winter. The first to get damaged are the finest feeder roots when it gets cold, with the pot size being another factor with bigger pot size providing insulating buffer. The next to get damaged are the next size roots and in extreme cold situation the big fat roots from the stem. The time it will take to green up depends on how far the roots got damaged. It can green up even if just the fatest roots survive but will need time to send out more roots from the fat roots.
Just keep it moist and wait. One of my fig trees greened up in early July while other trees were having small pea size figs then!

Give it chance and some time.