Check the writing on the cables to see if they are cat5 or something else. If they are cat5 or better they'll work for sure, but if they are original to an early 90's house they might be cat3 or cat4 in which case they'll probably work for gigabit Ethernet (anything will work if the cables are short enough) but it is more of a crap shoot.
If you want to replace the telephone bridge panels with something that fits in the same spot I think this
https://www.amazon.com/Legrand-Q-AC1058-Network-Interface/dp/B078FLT5S3
might be the right part. You may need to replace the keystones on the other ends too.