Can you update Apple TV to accept higher internet speeds than what is showen in speed tests

If these are different models, then they have different hardware with different networking components that will have different maximum speeds. There is no upgrade for that other than buying the newest model.

The “issue” is a bit trivial, as no service on Apple TV requires more than 25 Mbps.

Identify your Apple TV model - Apple Support

No, your internet speeds are governed by the package you get from your ISP and you network within your home. If you happen to own a home that is 1500 sq. feet or larger and you have multiple wi-fi devices (computers, streaming devices, telephones, tablets, smart tv's, and the list goes on and on) all of those devices are competing for bandwidth. You may not have adequate coverage throughout your home which means you may have a need for a Mesh network.

Likely because they are in different location and the signal strength received in each room is different. My home is about 2500 sq. ft. on a single level. My modem and router were on one end of the house and I have 4 Apple TV's throughout the house. I had a similar problem to you, where the Apple TV's that were close to the router got a good signal but the ones further out did not. This is called a bandwidth/coverage issue. I had to upgrade my network (by the way your routers ae very outdated now) to a Mesh network. If you are unfamiliar with Mesh networks please read this article and see if you may be a candidate, from your description I think you are!

I happen to use the Google Mesh network but there are many players in that arena no so if you decide to upgrade please look around. I like my Google Mesh, since installing it 2 years ago I've no zero issues and I support 30+ wifi devices in my home. I now not only have coverage all over the home but outside on the patio too which is really nice if I want to sit outside and watch Apple TV on my iPad or surf the net or whatever.

https://support.google.com/wifi/answer/7182746?hl=en