The storing of hyperlinks is fine and dandy as long as the site stays up

Saving the web page means you will always have it.

Looks like you want a bookmark manager, many self and cloud hosted alternatives exists, personally using Linkding! Some of them also support archiving which means they also save the content locally!

Pocket?

I bookmark them in Firefox and check to make sure the pages have been archived by the Wayback Machine.

A simple solution would be to load your links into a spreadsheet and make your notes in an adjacent cell.

Beyond that there are bookmark services and software: https://www.google.com/search?q=bookmarking+service&oq=bookmarking+service&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIGCAEQRRg80gEINDAyM2owajSoAgCwAgA&sourceid=chrome&ie=UTF-8

Personally, I'm completely opposed to anything outside of my personal PCs keeping track of my browsing habits.

Rather than just mailing you the link you also could mail the text snippet too. A bit more work, but more robust into the future. If the respective site goes down you still have the critical information.

So many options here;

Just press CTRL+D

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or use gmail and tags, then archive the messages so they don't 'take up space'

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or a notepad text doc in dropbox

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or google keep

Archivebox might be something to look at. Open source, self hosted, made for archiving websites.
So it not only keeps track of your mass of links, you can also snapshot/archive them when you add them. So if they ever were to go down, you'd still have a copy yourself.
https://archivebox.io/

Though to be fair, I have not actually tried it out myself. I looked at it a few times but I don't personally have a need for it so. Worth taking a look at though.