It doesn’t use XMPP or Matrix. It’s just an open source Discord clone.

You don’t need to calculate the average number of active users. If you do, it will be wasted resources and you probably will miss a few dozen.

Simply request the instance’s NodeInfo.

NodeInfo 2.1 (which Lemmy does implement) and I think 2.0 as well require implementors to provide correct user usage statistics. So you have total users and average active users per month/half year calculated on request.

This also means you can provide this service for other platforms that support NodeInfo.

Making a GET request to /.well-known/nodeinfo will give you the links to the instance’s NodeInfo documents.

In fact, you can recursively begin from some random known instance, get a list of other instances it is federated with, get their NodeInfo and repeat the process. NodeInfo also provides the name of the software (check schema).

You can use that.

FEP: https://codeberg.org/fediverse/fep/src/branch/main/fep/0151/fep-0151.md

Schema: https://nodeinfo.diaspora.software/schema.html