Why is my iMac stuck on the Apple logo during recovery?

Sadly this sounds like a failed drive or some other hardware issue.

see > If your Mac doesn't start up all the way - Apple Support

To run the Apple Hardware test, see > Use Apple Diagnostics to test your Mac - Apple Support

Also, have you considered recycling and then replacing the machine. At almost 15 years of age it is far past its prime. Even if you are able to resurrect it, it will still be the same age. With age in computers comes some major issues including:

• Not being able to run current versions of Mac OS, this is a major problem as third party developers simply will not develop their software for old OSs. That means eventually your third party software can't run or not be full featured.
• It has been classified as vintage by Apple many years ago. This means parts for it are largely not available so if something internal breaks you are simply out of luck.
• It's incredibly slow by modern standards, nothing you can do about that really.