flighty_sloth An open TCP connection does not drain power, all it is, is a state established in a number of routers for delivery of data between two endpoints. Your phone can open a connection and then go to sleep -- incoming data will cause the phone to wake up for the data to be delivered to the appropriate process, which can then process the data appropriately. The only thing that causes such a connection to drain power, is a very poor implementation that continually wakes up (or just remains awake) because the software developer was too stupid to just let it sleep.
I keep 3 persistent connections open (two applications) -- two IMAP IDLE for email push notifications, and one HTTP/SSE for Nextcloud notifications (https://gitlab.com/Nextcloud-Push/) -- both applications register <1% battery consumption, which is WAY less than gservices would draw if I had that installed (I don't).