Each Mac will notice the others on the network, but won’t volunteer to share files until and unless told to do so.
To tell your Mac to start up file shares (usually SMB sharing, but also possibly the being-deprecated AFP):
System Preferences > Sharing
Details: Set up file sharing on Mac - Apple Support
Other options include network-attached storage (NAS) servers all Macs share, and iCloud files which shares to and from iCloud.
Migration Assistant (mentioned in a reply above) is one-way, and seemingly not what you’re looking for.)
Handoff will work too, but I’m guessing you might want to look at the contents of the login and other directories across hosts, and Handoff doesn’t provide that.