How do you do server-side analytics?

I think the answer to this is two-fold. There is analytics for Monitoring and Analytics for business.

For monitoring and making sure the server is working well: Graphana, datadog and the like are good.

For business analytics (like building funnels and things that happen in the back-end). Mixpanel is a great tool for it and can be used by multiple teams (as they also have a FE counterpart that makes you able to get a more holistic view of a user, which is a big plus).

GA is a pretty crappy tool for the modern startup. It was developed literally 20 years ago to measure what at the time were static content websites(news sites and blogs) and it just kinda stayed that way 3 versions later.

The new GA4 Does allow you to also track things in the Back-end in an integrated way but it is very very new (i.e. features are missing, like a proper way to pass user_id to the events and documentation is very scarce). On the other hand they are picking up the slack and making mixpanel run for their money. GA4's main advantage is that it is free and super easy to share with, say, your sales guy or a marketing agency if you come to use one.

btw. Mixpanel has pretty expensive plans, in my day job we were once paying for it (9k USD per year) and then cancelled.... we didn't notice the difference. The paid features are really niche >>> you can get pretty far with their free features

I use newrelic for application monitoring (for python, but I'm sure they have nodejs available as well). helpful for looking at transaction counts, transaction times, and error rates. they have a free tier, would recommend.

sentry.io

I log EVERYTHING to Mongo and filter my way through

I kinda don't. I just increment a number in a db table for some stats and look at it from time to time.

I had faced the same scenario few weeks ago while I was setting up our SaaS infrastructure, but finally I decided to track everything in-house. I ALMOST went with Datadog's Log Management plan.

I didn't signup but from their website I see that it is possible to subscribe to Log Management only, which will be dead-cheap (advertised as starting @ 10 cents/GB).

You can use Prometheus for collecting/storing metrics and Grafana for visualization. It is easy to setup, maintain and use.