While this works for third party websites, just changing the User-agent string does nothing to convince YouTube, which is developed by the same corp developing Chrom(e|ium), that it's a Chrome. And it's mindbogglingly simple for YouTube to check it: Firefox (and its forks) lack Bluetooth API, File System API, Sensors (accelerometer and gyroscope), WebSerial, among many other HTML5 (mostly useless) features currently only available in Chrom(e|ium).
Yes, a Firefox extension could theoretically implement faux shims for Chrome-exclusive HTML5 APIs (e.g. setting a fake/blank navigator.bluetooth.requestDevice method before YouTube's frontend loads so YouTube's frontend could check it's not undefined when doing typeof), but some of these HTML5 APIs are actually used for YouTube's functionalities and they don't even required user intervention (e.g. accessing gyroscope/accelerometer sensor data, which is also only a Chrome thing for now), meaning any "pretending to be an available API" wouldn't work the same way when compared to an actual implementation of said API.
Also, there are codecs and Widevine (which is owned by Google as well). An extension couldn't possibly implement a support for a video codec that only exists in chrome, or the proper signature/keys to pretend to be a DRM. I imagine it's the trivia Google is weaponizing to serve high-quality versions of the video for chrome, with said high-quality versions using a codec that Firefox doesn't currently support.
This said, I proudly say I haven't used YouTube since I deleted my YouTube account (iirc) three years ago. I don't even use circumvention tools, I simply stopped using YouTube altogether. And I recommend that people do the same, because YouTube only exists and continues to enshittify as long as there's audience (both viewers and content creators in some kind of ouroboric relationship wherein creators keep uploading videos because there are viewers, and viewers keep watching videos because there are creators, none dare to think of leaving as Google makes the experience further awful for both). If you people continue using any platform from a big tech corp (YouTube, Facebook, Reddit, etc), you can't really expect anything other than enshittification, it shouldn't be so surprising, you know...