Full body workouts are amazing and work quite well for either goal of hypertrophy or strength. The ability to hit multiple muscle groups within one training is doable, but requires determination and focus. It is very important to also make sure that you focus on going to a closer to failure range a little more often in many of the exercises than normal (in order to produce the desired outcomes).
If your goal is a home workout with only barbell training, then there is no reason a standard Squat, Bench Press, Deadlift progression. The focus in a full body workout is to try to do you hardest workout in the time allotted. Each set should push yourself to higher RPE, in ranges of 7-9.
It would be easy to do one day in that order and reverse it on the second day of training. This would allow you to still train each exercise as often, but also allow you to have a day where each lower body training is allowed to be the "strength" focused workout since it will occur first.
As far as sets and rep ranges, you'll need to play this by ear a little, depending on how fast you can setup the lifts and recover between. I would aim for at least one strength set in the rep-range of 4-6, followed by a couple sets of 8-10 reps.
This answer focuses a lot on barbells because of the information provided, but I would also suggest if someone wants to do a full body two days a week and has access to the gym, Jeff Nippard published his training split for this on his channel and you can watch his video to get the breakdown as well as how to split it further if you'd like more days. But the focus is for 2 days at 45 minutes or less.