:: insert boilerplate about 90% of “error” messages in GSC really just being informational ::

--spammy links: ignore them. In fact you can snicker quietly, because linking to a 404 just makes the other site look bad.
--legitimate links: try a little harder to find appropriate redirects, if the same content now exists at a different URL. This also benefits humans who happened to have the old URL bookmarked. If you can find the new URL, and you are in contact with the other site, ask them to update their link. Otherwise don't stress about it.
--internal links: This one's on you. You need to fine-tooth-comb your site and make sure that no page, anywhere, links to anything that now returns a 404. Any standard link checker should be able to deal with this. Or, if the pages are hard-coded html and the URLs fit a recognizable pattern and your site isn't too enormous, do a comprehensive search in a text editor that does multi-file searches.

If Google claims that suchandsuch 404 URL is linked from some named page on your site, or they claim it's on the sitemap, and you've checked and it's no longer true ... ignore them. See above about information vs. error.

Incidentally, the Googlebot will stop requesting pages sooner if it meets a 410 instead of a 404. Other search engines don't seem to care. If the old URLs all fit a pattern that doesn't apply to current URLs, it should be easy to apply the 410 globally. Make sure you have a nice 410 page for humans. Depending on your site, you might even use the same (physical) page that you use for 404. But you have to say so (ErrorDocument directive, or equivalent in non-Apache servers).

Do nothing. 404 generally has no hurt value. If you want to clean up your raw logs, and have the time and energy to write the code, redirect to 410 and the search engines will drop the attempts faster. DO BE AWARE that no search engine will ever forget a URL it has met (your site or a back link) and will try again YEAR ON YEAR into the next century. Which merely means you keep the redirects in your .htaccess FOREVER. If you do them.

Or ignore them.

I look at this way: It is not up to ME to clean up their crawl budget. My site is KNOWN (by their crawl). It might change from time to time (I have no contract to say which pages are REMOVED and there are times when a 301 is not desired, much less necessary), and I certainly have no responsibility for links from exterior sites who don't keep up with my site, or have bad coders who inject typos into hyperlinks.

Returning a 404 is less stressful, and certainly bandwidth friendly. (mine is 125 CHARACTERS)

You don't want to loose traffic. Create a redirect. 2 choices:

1. just redirect the person to the new page assuming you know what they were looking for. If they are getting a 404 for tacorecipes.htm and you can redirect them to tacorecipes.xml you're done.

2. load a page that explains the problem to them. The page you are looking for has moved. Please inform the webmaster that referred you here, or re-bookmark the page. You will be redirected in 15 seconds. Then the page refreshes to the new page.

welcome to WebmasterWorld [webmasterworld.com], LeisureMan!

You will be redirected in 15 seconds. Then the page refreshes to the new page.

are you suggesting a 200 OK response containing a meta refresh?