You have two choices.

You can be completely independent and book your own hotel and visa (which will probably be more expensive overall) but eliminate any delays or risk. At 1am, you will simply breeze through immigration and be in your hotel probably within 30 minutes of touchdown.

Alternatively, you can take your chance with purchasing an STPC package from Ethiopian (you won't be automatically entitled to this as you are on a TK-ET connection). You will be at their "mercy" as to which hotel you are assigned - probably the Radisson Blu as a Business Class passenger since the Hilton has a number of rooms currently under renovation, but for the same reason if the Radisson is full you could be placed somewhere significantly sub-standard. The "visa" is included as part of the package (not really a visa but rather a visa exemption) but you will be at ET's mercy with regards to ground transfers. This will be cheaper, but on a short 8 hour overnight, I'd personally prefer to be completely independent and stress-free rather than worrying about which hotel they are going to put me at.