I used Pathfinder years ago and remember doing this.
Looks like this is built into Pathfinder — from Pathfinder’s help:
“Enable Finder’s ‘Remove from Dock’ – Choose this menu item from Path Finder > Finder to allow the Finder icon to be removed from the dock. Once enabled, right-click or control-click on the Finder icon in the Dock and choose “Remove from Dock.” This will allow the Finder to run silently in the background. The Finder will necessarily reappear in the dock every time you restart your computer.”
Replying to my own topic after hearing back from support.
The following option was removed for newer macOS versions since Apple made some changes within the operational system. This option only works for macOS versions such as Mojave and earlier.
So anything after Mojave doesn’t support hiding the dock icon - at least not in a way Path Finder can do from a menu option.
Which leaves me still looking for a solution, I guess.