I doubt you can reliably determine if on Wifi or not, although of course the carrier handling that phone would know.
The LIDB data will consist of a field that marks that phone number as a landline, broadband (aka VoIP), cellular, etc.
There are some 2FA implementations you come across will look up whether a number you're trying to enroll is classified as anything other than cellular, and if so, it gets rejected.
Based on what I've read, some video games are able to determine if you're using a prepaid plan or post paid. I suppose they might just look up the carrier to determine that since it doesn't seem like that level of granularity is available. And the port trick may work there as well.
I also have a Google Voice-backed number (since before Google acquisition, when it was Grand Central), and every now and then I find a site that doesn't accept GV numbers for 2FA. A recent example was Simplisafe.
Does anyone know where "Fraud Risk" and "Textable" come from in unlec's database? My number has fraud risk = high, and textable = No -- even though text works just fine via GV, and it's a personal number with minimal use, so no reason for flag (other than some companies not liking virtual carriers).