I'm running my instance with lots of bridges in a 3-core 4GB server, paying about eight euros a month for it. Synapse runs just fine, but I'll probably switch to the Rust impl when it's done.

If you want to go cheaper and have only 300-400 Mbps of bandwidth, I've heard lots of good things about this provider:

https://contabo.com/en/vps/

Not those two (and I know those are especially large), but we are in many 5-10k rooms, including bridged Freenode rooms which are known to be some of the worst offenders.

Note that many significant improvements have landed very recently, for instance the chain cover stuff which significantly improves handling of rooms with frequent membership changes (such as the aforementioned bridged IRC rooms).

The federation is chatting around the clock. Remember, joining a Matrix room means that your server needs to handle all of the room's traffic. And 25 users can easily be in a lot of large rooms. However, each room only needs to be handled once, so if more of my users join a room in which my server is already participating, the cost doesn't increase.

That said, this isn't an average but a spot value. It frequently falls below 8% (though typically stays above 5%). Note that this is a cheap and relatively weak VPS.

I'm not saying Matrix is terribly lightweight. I'm saying you can easily run a small personal instance on a cheap machine without any performance problems.