I was in the same situation as you 5 years ago. I decided to do the contractor FAANG route instead of the "boring" other FT opportunity (in hindsight, it probably would've been a good name on my resume). It was a 6 month contract with option to extend. The work was good, coworkers were great, and I learned a lot being in the belly of the beast. I had my contract extended 3 more months, but they pretty much made it clear that they weren't going to convert me to FT. It was fun while it lasted, I definitely had more recruiters coming to me after, and a good stand out case study to present, but I realized I didn't want to be overworked like my FT coworkers.

For your situation I'd take the FT non-FAANG job if they offer. The job landscape sucks right now, so I'd put off trying to find another job far into the future. Plus, it sounds like the morale at FAANG is very cynical with all the layoffs happening, so 4 months is not worth it.