Game Boy emulator with a full debugger?

VBA-M has a bunch of debugging tools under "Tools" menu, including memory & tile inspectors and a disassembler. It even has support for GDB. I didn't test with any frontends like gdbgui, or VSCode's GDB support, so YMMV, but the other built-in tools look pretty decent.

Go to the releases section for a build for your platform (arch linux also has it in AUR, for easy install in package manager.)

Here it is running some of the tools on a Mac:

No$GBA is for GBA games; you want NO$GMB. Note that it's very buggy, and without a registered version (which may be impossible to get legitimately) rather crippled.

bgb is free and is very similar to No$GMB, but even buggier.

VBA is supposed to have a debugger, but there are a million different versions out there, so good luck finding the right one.

Check out the site GbaDev.org and look on the forums. This is the best spot on the web for GBA or even GBC questions. I can tell you that there are many versions of VBA and no$ out and about. The No$ you want was technically a pay for version, but Martin Korth hasn't been answering emails or anything for years now and I'm not sure of its status anymore. I can also answer some questions for you personally if you'd like or help you with the debugger.

I was able to go to the no$ main website, download the windows version of no$gmb, and use it to debug when run in B/W mode - should be sufficient for you needs. F12 opens roms, F2 toggles break points, space traces, F3 steps over, Ctrl-G takes you to an address (or symbol), and Ctrl_B allows conditional break points (by far the most powerful feature for you to use.) For instance, (3000)! would set a read/write breakpoint on address 0x3000. (0300..03003)! sets on a range. As you are looking for specific address changes, this is what you want.

If you just want to debug your old gameboy games you can also use bgb which has several debugging options such as tracing, breakpoints, profiler and a lot more.