sadnehs I was wondering if I could try a second desktop environment, on top of Budgie.
You can install Gnome or Xfce on top of Budgie, here is the guide. We do not recommend mixing Plasma with others though. If you really wanted TDE, I suggest you looking to another distributions that provides it. Solus does not have it
sadnehs Is there some way a DE can be installed from source?
The only you get TDE on Solus is only by compiling it youself, here is their official guide. As always with stuff not in our repository (especially desktop environment), do not expect any support from the staffs.
sadnehs I'm under the assumption eopkg is entirely custom to Solus.
Yes, it is our homegrown package manager.