Help with operating system install

I have iMac late 2013 with Catalina on it.

You have to get Catalina off of it first, by erasing the startup drive. Did you do that?

Moreover, are you sure you want to do that?

What are you trying to achieve by doing this? I ask because:

1. High Sierra is an earlier version of macOS than Catalina (and by many measures, Catalina is consider a better version - in fact, if I recall correctly, High Sierra will always show an OS upgrade to Catalina as pending in the App Store) and all software supported on High Sierra should be supported on Catalina;
2. High Sierra's implementation of APFS was a bit incomplete (one reason that High Sierra always wants to upgrade;
3. A late 2015 Retina iMac supports macOS versions from Mac OS X 10.11 El Capitan to macOS 12 Monterey.

So I can't think of a natural reason why you would want to downgrade to High Sierra...I could perhaps understand swapping the hard drive (unless it's the original HDD - which is really old at this point), but you don't need to downgrade to do that.

Why not simply restart in the Recovery Partition and install Mac OS from that? If you continue to have an issue take it to an Apple Authorized Service Provider and this should be a relatively easy thing for them to do.