Ably Realtime

Key thing to understand here is that you are hosting data & logic somewhere. Socket.IO requires you to host and manage a dev server somewhere (as the previous suggestion mentioned Heroku is a good choice)

However, It's not really in keeping with the serverless world that Vercel provides and its a headache to scale and manage. We (I work at Ably) have a bunch of open source examples of how all this works. Ably provides serverless N to N connectivity, along with first class integrations into serverless functions on AWS, Azure, cloudflare and GCP. This allows you to build a realtime, serverless system that you can scale without any pre provisioning.

Nothing is totally free but you can get away with the free tiers on all of these services for a lot longer than you may think.