There seem to be some 500 allowed tags on MY. Where do I find a list of them. (When I click on tags, I get a screen with a dozen and an option to click through 50+ such screens.)
The tags list, which shows 36 at a time, is the official way to browse tags. If you type some text into the box (at least three characters), it acts as a search/filter. There might be a way to get the full list through the SE API, which I don't know much about.
This interface is definitely Not Ideal. Some time ago, people here started an effort to organize our tags logically rather than by frequency or alphabetically: Systematic list of tags. Browsing the answers there might help you find what you're looking for, though the project is incomplete. (Feel free to add to it! It's Community Wiki for a reason.)
That question contains a list (now out of date) of all tags on the site. That list was generated somehow. Perhaps that code still exists somewhere.
That tags screen is the official way to do it, i'm afraid. To be precise, it actually shows 3 dozen on a page.
You can also use the search box on that page to try and find a specific tag, but be prepared to try several spellings.