First of all don’t use Youtube. I haven’t used Youtube in years in Palemoon and I don’t miss it. Use a wrapper like Invidious or https://piped.kavin.rocks and then use RSS to “subscribe” or follow channels.
As an example I’m going to use Arlo, who’s a Nintendo fan channel with a puppet. Here’s the Invidious page for him (snopyta instance):
https://invidious.snopyta.org/channel/UC-9QiiVaViuqMhLp1XEwdxA
If you load that page and look at the URL bar, you will notice an orange RSS/Atom symbol next to the bookmark star on the right side of the URL bar. Additionally on that page below the top banner on the right hand side you’ll see a black and white version of that symbol.
RSS and Atom are feed systems for websites, they are saved as bookmarks either in your bookmark menu or your bookmark toolbar. Pay attention to URL bars of websites because sometimes you’ll see the feed symbol meaning you can subscribe to that website’s feed. This is an excellent and quick way to check if a site has updated, or if any of the updates are worth checking out!
For the sake of this guide we’ll click the orange symbol. If you really can’t find it feel free to click the black and white symbol instead. It should open the following page:
https://invidious.snopyta.org/feed/channel/UC-9QiiVaViuqMhLp1XEwdxA
What should then load is the feed. Palemoon is unique in modern browsers in that it doesn’t force you to download an extension or run an external program to read RSS/Atom feeds. My guess is that it’s bad for Google’s ad revenue if you don’t visit the website regularly.
Click the “Subscribe Now” button in the top section of the feed, and make sure the default save location is “Live Bookmarks”. Save it like you would with any other bookmark.
Now go to the location where you saved the bookmark and click it. It should open a dropdown with the latest videos posted to Arlo’s channel. You can do this with any channel on Invidious or Youtube.
I avoid Youtube like the plague but I’m going to include this last bit for those that want to use the same trick:
Arlo’s feed on Youtube:
https://www.youtube.com/feeds/videos.xml?channel_id=UC-9QiiVaViuqMhLp1XEwdxA
Google makes it much more tricker as they hide the feed from you. You’ll have to find out the channel ID, in this case, “UC-9QiiVaViuqMhLp1XEwdxA” and substitute it in the URL.
I really enjoy using RSS to make my life easier and be able to check out multiple sites/channels for updates. Use it whenever you can!
Later edit: As an additional bit of quality of life, if you add “&quality=dash” to an invidious url to a video you’ll enable the resolution option on the video dash. This will often help you watch newly posted videos that won’t normally load sometimes. It may start playing in a low resolution but you can then set it to something more acceptable.
For example: https://invidious.snopyta.org/watch?v=OFNZ3J0w7h8&quality=dash
