How do I find my file server on Mac mini to use in transfer to a new Mac?

Sorry, your question is not very clear.

Macs don't have File servers in and of themselves. They can be used as File Servers if set up for that.

What exactly are you trying to do?

If you are trying to access the Mac mini over the network to transfer files to the new Mac, make sure File sharing has been set up correctly and it should appear in the new Mac's Finder under Network.

click here ➜ Set up file sharing on Mac - Apple Support

If you mean something else, then please explain in as much detail as possible.

If you are trying to migrate from the old Mac to the new one over your local network, I don't believe you would set up the old Mac as a file server in the usual (Preferences/Settings panel) way. You run Migration Assistant on both Macs – and it would set up whatever arrangement it needed.

Transfer to a new Mac with Migration Assistant - Apple Support

However, migrating over Wi-Fi might not be the most reliable way to do things. I'd suggest migrating from an up-to-date backup of your old Mac, as described in the User Tip to which rkaufmann87 linked.

Simply follow the directions in Setup Assistant and Migration Assistant. You MUST and I mean MUST have adequate storage on the new Mac mini to migrate. If you purchased a based model with only 256GB of storage and the old Mac had more that 256 GB (more likely 200 GB) of data stored on it you cannot migrate.

I mention that because many buyers are buying the entry level MM which has only 256GB of storage on it which often is simply not adequate!!!!!!!!!!!!

If you follow the directions in the link noted above your migration will be fast, simple and trouble-free.

As mentioned above your original post is NOT clear. Macs do not have file servers so if you mean something else please do a bit more research and re-write your question.