I found an article on the topic.

Proxidize

Passive OS Fingerprinting (TCP/IP Fingerprint)

Discover how passive OS fingerprinting identifies your OS via network traffic, its impact on proxy users, and methods to spoof OS fingerprints.

Essentially, browsers do not come packaged with their own low level internet browsing code. AKA the TCP/IP stack. Instead they rely on the operating system's built in features to connect to IP addresses. This code behaves differently between different browsers and so it results in an identifiable fingerprint. You can follow this link to see what it might look like:

BrowserLeaks

My IP Address

The main tools for checking IP address privacy. Showing Your IP Address, Reverse IP Lookup, Hostname, and HTTP Request Headers, Your Country, State...

It sounds like this would be easy to solve. Just don't do that. Statically link OS independent TCP/IP code to package it with the Tor Browser and ignore the OS's version entirely. I'm not sure what the problem with this would be, but my guess is that this would require bypassing important OS security features like firewalls and network interface drivers. I imagine that most operating systems would take issue with random userspace programs doing that, and Tor doesn't want to run as an administrator. I haven't tried to write any web servers or web clients so I don't have any idea what is and isn't possible.