Should I mention my YouTube channel in my query letter? I'm just starting out, so would it be helpful at all? Also, I know querying authors should have a website-- could a YT channel stand in lieu of that?
Last bit first: Nope, a page on YT or [insert social media platform] does not take the place of a website. Just get a dang website. It doesn't have to be fancy, it doesn't have to be large, it doesn't have to be expensive -- even if it is just a landing page where you can have a little bio / "about" and links to all your different social media and contact info. Even if that's ALL you have on it -- fine! Consider it a modern day business card, saving your domain name so nobody else snatches it. You can add more and make it fancier once you have books coming, and I promise you will be glad that this process is already started once that time comes.
(OR, you know. Don't, I guess. Listen, I'm not your mom. Do I think having a website before you even have books is a good idea? I do. But so what? If you don't want to, OK, do it later then. Nobody will offer rep or not based on whether or not you have a website started when you query, so whatever. But once you are more established and you actually have books coming, etc, it will become quite important, so as long as you know that, do what pleases you. But maybe put a bio and LinkTree in your YT or other socials at least?)
With regards to mentioning YT (or any social media) in your query:
-- If you literally just started, the page is basically empty and you have no idea if you will post regularly yet, I'd refrain from mentioning or linking to it until there's something there to see. Nothing sadder than a page with tumbleweeds rolling across it, yanno?
-- If it is something that you do regularly update and you think is a good reflection of you, by all means put it in the signature line of your query, alongside your website, other handles, etc. But no need to call it out IN your actual query letter -- that's valuable real estate where you could be talking about the important stuff, like your BOOK! :-)
-- The exception. when you really SHOULD mention it in the query, is if it is literally, like, your job description, you make money at, or it gives you a big platform that might boost the audience for your books -- in which case it would make sense to add to the bio section of the query. "In addition to writing books about the social lives of animals, I run social media for the Cincinnati Zoo and have a YouTube channel with 1.5 million followers" -- seems like good stuff to mention in your bio to me!