@jonp recently confirmed recently that there are plans to be able to adopt existing TrueNAS systems into HexOS for management, but that's not something that is likely to be implemented soon.
If I were in your shoes and I wanted to make things happen quickly I would build your second server and install HexOS on it, copy all your files and such, and then convert TNS01 to HexOS as well.
As far as how it all works, HexOS exists on an equal level as TrueNAS' GUI interface, and both of those talk to the TrueNAS API which is a layer down, and is what actually does the work. Both interfaces work side by side. They're like siblings in the way that they relate to the TrueNAS API. You could think of it as having two options for your user interface for TrueNAS.
Here is a diagram to illustrate:
On the left is a normal TrueNAS install, and on the right is HexOS. The HexOS installer has the HexOS command deck web connector added, and that's about the only difference as far as the actual installer goes. The rest of the interface is handled from the Command Deck web app, which is cloud based.
A fully local HexOS UI option will be coming before full release. It's unlikely to be at full feature parity with deck.hexos.com. Details are TBA though.