How can I delete locked networks on my Mac mini running Sonoma 14.4.1?

Those other networks are Wi-Fi networks detected automatically by your Mac. They are not locked but password-protected (the lock icon.) You cannot remove items in the “Other Networks’ section. You could only “forget” a Wi-Fi network in the “Known Networks” section.

I don't think there's anyway to eliminate them, you're not connecting to them, they're just "advertising" themselves.

You’d have to connect to that network to be able to forget it. Yet, I think that it would then appear in the “Other Networks” section afterwards.