The most important privacy consideration is who gets to see this data. If you just use it internally and not share it with 3rd parties, then you are already ahead 99% of the businesses in terms of privacy.
To keep the data for yourself, it's best to use a self-hosted analytics platform. Most of them also allow for more granular settings, where you can set exactly which data is stored and how.
It depends on what you need to track. For my startup the thing is that open-source developers are sensitive about data and do now want to share them with you. As pointed there: https://news.ycombinator.com/item?id=35358384
For the website you can create a cookie cosent or use a privacy focused alternative like https://matomo.org/
Is anonymizing data not good enough? That's what most of these trackers do. Something like Firebase Analytics even refuses to track if there are below a certain number of users.
You can check out Simple Analytics too https://www.simpleanalytics.com/blog/why-simple-analytics-is...
Quite a few options out there https://wideangle.co/blog/best-web-analytics-in-2023
Hash the ip address + user agent + year/month, use that as a unique identifier for the month (note that you only need to store the hash)
Regular analytics solutions like Google Analytics and its many competitors pose negligible privacy risks to visitors and clients.
You can use Usermaven.com. It’s a privacy friendly web analytics and product insights solution.
Block the metrics system from accessing PII like IP addresses or usernames.
You can use cookieless tracking.
Track signups and pageviews
I use a service called Plausible for this - they are privacy focused (do not even use cookies) but there are some drawbacks (like not being able to really know MAU since user identifiers reset daily)
https://plausible.io/privacy-focused-web-analytics