I cannot stay connected to the game for literally more than one minute at a time, after which I get "Server not responding" message and a disconnect. It's not my connection (20Mbps down, 2Mpbs up). I've tested on numerous sites, other programs, and MMO games.
Please resolve this a.s.a.p. since the winter event requires to be run every day to get the final prize after 25 days.
Your connection is only as good as your ISP's hardware. Your data, though, travels over segments that aren't controlled by your local ISP.
Connection speed and the way it's overhyped is, IMO, merely a marketing pitch sold to people who really don't know how the internet actually works, but again, that's merely my opinion. YMMV
Testing on "other sites and MMOs" is hardly a valid diagnostic because the issue may be the route to STO's servers, which may or may not follow the same route as other data transmissions (which, given the absolute multitude of destinations for the internet, would likely be a different route).
Anyway, there have been several users in the northern CA area that have been reporting issues. Try running a traceroute and a nettest as suggested in the troubleshooting sticky at the top of this forum to at least have a baseline of what's going on between your PC and the servers, and to see if your net connection is performing anywhere near as advertised.