Is there any CDN provider able to offer some sort of WebSocket caching either via "Edge Workers" or other mechanism?
I would like that some WebSocket requests that we make to be able to serve them as close to the user as possible without us setting up our entire infrastructure in multiple datacenters.
No, there is no way to cache WebSocket messages - e.g. the protocol does not have any "addressable" resources as e.g. HTTP. HTTP has more built in design for caching in the protocol, e.g. GET requests are typically cacheable but not POST requests and you can add cache related headers to the requests, e.g. how long it can be cached and so on.
For this reason, I would recommend to use HTTP instead of WebSocket unless you have a use case where you really have to use WebSockets. With HTTP you have access to all CDN and proxy infrastructure that is available globally.
It is getting more and more common to use e.g. Server Sent Events, HTTP/2 streams or possibly GRPC for use cases where WebSockets was used before. The upcoming WebTransport protocol will probably be the replacement(?) - at least when most other traffic is HTTP/3.