That was me! And I stand by what I said. Recommend OP takes a day train + normal hotel in Scotland.
But, if you're determined to do this anyway, you might consider keeping your hotel room in London for the extra evening just to have a place to relax and come back to, take a nap and a nice place to freshen up before the train ride. As the train doesn't depart until nearly midnight (assuming it leaves on time), we were really tired and exhausted from being out all day long after checking out of our hotel at noon. The "lounge" at Euston is serviceable, but pretty bare bones. We took showers to try and freshen up, but it was kind of gross and not super clean.
And check the dimensions of your luggage carefully.
https://www.seat61.com/sleeper-to-scotland.htm has the exact storage compartment sizes - there is no "give". We had a room with a double bed. They'd *just* introduced the new car design and we didn't have that info. Our bags didn't fit and we had to tetris them into the tiny path between the bathroom and bed, which was very awkward.
The staff were nice. You won't see much because it's dark out and you should be trying to sleep. Our teen was in another suite, but being just 1 person, had plenty of room.