How to tell if a project has real legs?

For something that's more Meta specific, I would avoid any team that's trying to build a separate app. It's kind of sad and ridiculous, but it's just not in Meta's DNA anymore to build successful separate apps - They always get shuttered, which usually leads to bad career growth for the engineers on it (especially if you're targeting E6). Google has a reputation for canning new products often, but they at least have a constellation of home-grown apps like Gmail, Google Maps, and their office suite (Docs, Sheets, etc). Meta has had to rely on acquisitions.

I am also skeptical of teams trying to add new features to Big Blue like the LinkedIn competitor and the Fandango competitor. Facebook has historically not done a good job of becoming a "super app", and these teams also often get shuttered.

How can I figure out during the team selection process if a team is doing its due diligence on gathering context and proving out business value

This is really tricky unless you have experience dabbling in product manager behavior. To help with that, I recommend going through this discussion around improving product vision as a software engineer.

That being said, I have 3 pieces of advice here:

1. Talk to the PM - If applicable of course. For E5s, I have generally seen the strong ones have a good relationship with their PM.
2. Go through product vision materials - PMs (and sometimes E5s/E6s if they're hybridizing as a PM) will generally write high-level Workplace posts detailing the product direction of the team (I have written several of these myself). Start with those, and you can go deeper from there by going into Quips/Google Docs.
3. Look at the metrics - Meta is all about using data to back things up. I would be skeptical of a project without much data behind it.

... or if its just building them for the sake of building them?

Hehe, no team believes they're doing this, and if they do, they won't tell you. This is why getting this signal is hard: Your read depends a lot on how good your PM hat is.

I just realized that we recently released a video on how to figure out if your team/organization is important to a company. You can watch it here: https://www.jointaro.com/lesson/9OwPRwFFSMvEoVj6Zt5Q/how-to-figure-out-if-a-team-is-important-to-a-company/