First, it should be noted that the only part of webCoRE that depends on the cloud is the piston editor. Once created, all pistons run locally on Hubitat. So, the outcome is the same either way, and hosting the editor locally might be more work to both set up and maintain than it is worth--your choice, of course.
If you wanted to try, I'm not aware of any newer guides than the ones in a previous thread on this subject:
Towards the bottom of that first post, you will find guides for setting up the editor on either a "bare" Linux server like Raspberry Pi or inside Docker on any supported OS/hardware combination. As noted in these instructions, you will need to point your Hubitat webCoRE installation to use custom URLs when you're done. Otherwise, there is nothing else to do on the Hubitat side, as Hubitat itself is not capable of hosting the editor on its own (which is why you need some external server--whether it's the cloud editor or one you host locally). But again, execution is ultimately local either way.
