People have done the TA on a massive variety of different bikes, including electric, cargo, touring or full-suspension mountain bikes, but the ideal tool for the job in our opinion would be either a bikepacking specific bike or a hardtail mountain bike. These bikes are the perfect balance between capability, durability and weight, all which are significant considerations for anyone looking to do the TA. These bikes will have a tyre size usually between 2-2.6 inches, and either a 29 or 27.5 inch wheels, which are the best options for a balance of efficiency and comfort. For most people, a bike like the Surly Bridge Club or the Surly Ogre would be a great bike for this sort of adventure.
Bikepacking bikes tend to have a much larger range of mounting points than a hardtail, making it easier to attach a variety of things to your bike, and are usually rigid and made of steel for the utmost durability. Hardtails on the other hand have the benefit of having a suspension fork at the front for a little more comfort/control on the rough stuff, as well as either aluminum or carbon framesets making them more lightweight, both for the trade off of being less durable, and less practical for attaching gear.