The desktop issue was an intentional change that happened sometime in like 2017 or so.
The original functionality of the quality selector was to throw out whatever video had been buffered and start redownloading the video in the newly selected quality. All well and good, but that causes a spinning circle until enough of the new video arrives.
The "new" functionality is to instead keep the existing quality video in the buffer and have all the new video coming in be set to the new quality. The idea is that you would have the video playing, change the quality, and it keeps playing until a few seconds later the new buffer hits and you jump up to the new quality level. Combined with the fact that YouTube only buffers a few seconds of video (a change made a few years prior to this; back in the Flash era YouTube would just keep buffering until you had the entire video loaded, but that was seen as a waste of both YouTube's bandwidth and the user's since there was always the possibility of the user clicking off the video; the adoption of better connection speeds, more efficient video codecs, and widespread and expensive mobile data caps led to that being seen as the better behavior for most people) and for most people, changing quality is a "transparent" operation that doesn't "interrupt" the video.
In general, it's a behavior that seems to come from the fairly widespread mid-2010s UX theory that it's better to degrade service or even freeze entirely than to show a loading screen of some kind. It can also be seen in Chrome sometimes on high-latency connections: in some cases, Chrome will just stop for a few moments while performing DNS resolution or opening the initial connections rather than displaying the usual "slow light gray" loading circle used on that step, seemingly because some mechanism within Chrome has decided that the requests will probably return quickly enough for it to not be an issue. YouTube Shorts on mobile also has similar behavior on slow connections: the whole video player will just freeze entirely until it can start playing the video with no loading indicator whatsoever. Another example is Gmail's old basic HTML interface versus the modern AJAX one: an article which I remember reading, but can't find now found that for pretty much every use case the basic HTML interface was statistically faster to load, but users subjectively felt that the AJAX interface was faster, seemingly just because it didn't trigger a full page load when something was clicked on.
And, I mean, they're kind of right. It's nerds like us that get annoyed when the video quality isn't updated immediately, the average consumer would much rather have the video "instantly load" rather than a guarantee that the video feed is the quality you actually selected. It's the same kind of thought process that led to the YouTube mobile app getting an unskippable splash screen animation last year; to the average person, it feels like the app loads much faster now. It doesn't, of course, it's just firing off the home page requests in the background while the locally available animation plays, but the user sees a thing rather than a blank screen while it loads, which tricks the brain into thinking it's loading faster.
This is also why Google's Lighthouse page loading speed algorithm prioritizes "Largest Contentful Paint" (how long does it take to get the biggest element on the page rendered), "Cumulative Layout Shift" (how much do things move around on the page while loading), and "Time to Interactive" (how long until the user can start clicking buttons) rather than more accurate but "nerdy" indicators like Time to First Byte (how long until the server starts sending data) or Last Request Complete (how long until all of the HTTP requests on a page are finished; for most modern sites, this value is infinity thanks to tracking scripts).
People simply prefer for things to feel faster, rather than for things to actually be faster. And, luckily for Internet companies, the former is usually much easier to achieve than the latter.