But, since I'm relying on other servers, am I leaking any info? I think YES. But what are they exactly? What data can a server monitor when I'm using that server?
Aside from data which already mentioned, the server also knows when you open your Electrum wallet. The consequences isn't bad as exposing your address, but they'll know when you wake up (if you don't use VPN/Tor) or estimate country where you live (if you use VPN/Tor).
Any light wallet connecting to a server will more or less leak that same info.
Closed-source wallet with their own protocol might leak more info, such as user behavior.