Animation studios. I know for a fact that Teen Titans was animated in Flash/Animate for its entire life, for instance; that’s directly from a former co-worker who was the animation director there. Lots of small productions, too. Animate is a lot cheaper than Toon Boom Harmony so tons of hobbyists use it.

The only difference between Animate and Flash is that SWF export got dropped eventually. And a haphazard smattering of new features got added.

You don’t play FLAs. You load them into the editor and output SWFs. Or various video formats. There are reverse engineered SWF players, most prominently Ruffle, but this is the first I’ve heard of anyone parsing FLA files.

FLA is the source format, it is to a SWF (or other video file exported from the editor) as a PSD is to a JPEG, or a .c file to an executable program compiled with all debug info off.

OK, my mistake on .fla vs. .swf ...

so the story is that Flash basically disappeared from the web, but evolved into a tool to do more general/extensive animation (Animate) that continues to be used today even though the output is (essentially) never .swf files? is that more or less correct?

Somewhat.

Flash started life as a general animation tool with a highly-compressible vector output format and a browser plugin to play them. And maybe some basic interactivity, I never touched it until version 4, when it definitely had pretty rich interactive capabilities even though you had to program it all via repeatedly hitting a dropdown menu with all the commands in it. 5 was a big improvement on that front with freeform textboxes instead.

Flash kept being used for animation while also being used for an increasingly large amount of interactive stuff on the web and desktop. Adobe bought Macromedia pretty much entirely to get it and started trying to build a write-once, run-anywhere programming environment out of it. Like Electron, with all its faults of being a resource hog with the added bonus of regular security holes that only Adobe could fix at a snail's pace.

Apple decided not to let the SWF player onto the iPhone's app store, officially citing the resource hog and security hole problems. People stopped using Flash to make interactive experiences. YouTube stopped delivering video as a Flash player streaming Flash's streaming video format. People kept on using it to animate.

Some time after this Adobe renamed Flash to Animate. People kept on using it to animate. I didn't, I'd quit animating by then.

Some time after that Adobe removed the ability to export SWF files. People kept on using it to animate.

And some time after that Adobe said "fuck it we're done with this thing, we've barely been adding any new features for a while, we're gonna stop supporting it and turn off the auth servers". People who were still using it to animate screamed. Loudly. And Adobe turned around within a day and said "uh okay well I guess we'll, uh, keep the auth servers running and, uh, maintain a skeleton team to fix bugs for a while".

One month after that, some dude made a post on Newgrounds - one of the major online centers for Flash stuff, both during the 2000's boom and the modern day - about his clone of the Flash editor, that he claims is capable of reading Flash source files. And here we are.

tl;dr: pretty much yes except it was always an animation tool from the very first days