I am relatively new to blockchains and I am wondering if on popular cryptocurrencies all information persists forever? If so wouldn’t grow the disc space requirement for every node by time? Will this become a problem in the near future?
Yes, assuming the chain itself doesn't die.
Dying means all of the nodes hosting stop "seeding" it to new nodes that want to join the network.
Most blockchains don't prune old transactions, though there are exceptions, including some that compress the entire blockchain state into a single ZKProof.