SSD or logic board failing on Macbook Air Early 2015?

While booted to your external drive have you noticed if the internal SSD disappears from the bus? If the internal SSD disappears from the bus, then verify the physical SSD is no longer seen in the System Profiler under "SATA" and "NVMExpress" depending on the type of SSD used. This is the best way to determine if the internal SSD is failing. You may want to "exercise" the internal SSD a little bit as well. Plus many times an SSD may fail by putting the laptop to sleep and waking it up.

If you can boot to the internal drive (either normally or into Safe Mode), then check to see if there are any Kernel Panic logs on the internal SSD. Kernel Panic log file names begin with "kernel" and end in ".panic" and can be found in "/Library/Logs/DiagnosticReports". Post several of the Kernel Panic logs if they are available. If you cannot boot the internal SSD long enough to access the logs, then you can access them while booted to the external drive, but you will need to locate the mount point for the internal drive which can be a bit difficult to determine with macOS 10.15+ which includes multiple volumes.

Try running DriveDx and posting the report here using the "Additional Text" icon which looks like a piece of paper. Apple SSD's don't contain a lot of useful health information, but you never know if something may show up.

You can also try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics won't detect most drive failures.

Since the laptop is working while booted to the external drive, I would say the internal SSD is most likely failing. An SSD is much more likely to be the failure point than the Logic Board in my own personal experience assuming the laptop does not have any liquid damage (happens to the majority of laptops I repair). These methods are the best way to determine an SSD failure --- unfortunately SSD failures are very hard to detect.

Either the logic board or the SSD could be faulty. It is not possible to isolate one from another without substituting parts. For example, you might remove the flash memory module, place it in an external enclosure, and test it using a Mac known to be good. If it fails, you found a problem. Not necessarily the problem, but that's the nature of troubleshooting.

Opinions don't really matter. The only conclusions that can be drawn will require physical disassembly, parts replacement and testing. It's up to you to determine how much time and effort you want to invest. As far as I know Apple still provides free Genius Bar diagnosis, but getting an appointment can be difficult in some places. Start here: Get Support

That's what I would recommend. If it doesn't work you could always sell it.