Unless the protocol is connectionless, the server will always know at least the user's online status.

I have to use Slack for work, and the way I solve this is to have my client not send typing notifications, and have the client running on my server and repeatedly sending activity notifications all the time, so I always appear online and present to Slack servers.

I can prevent Slack from knowing when I'm really connected only by being connected all the time and always pinging my activity status in periodic fashion 24/7, so that from PoV of the server it's not possible to determine anything about my actual activity or online status on my workstation, because there's no relation to real-life status.