Are there any limits? Not talking streams (which is 200), but actual websocket clients.
There is no limit on the number of connections. Open as many as you need (within reason). However, note that rate limiting applies per IP address.
For WebSocket market data streams the limit is
A single connection can listen to a maximum of 200 streams.
Note that it’s a limit on how many subscriptions a single connection can have, not the limit on the number of connections.