I've done the Royal Day out tour a couple of times. This tour also includes a visit to the Queen's Gallery and the Royal Mews. On both occasions I particularly wanted to see the exhibition at the Queen's Gallery and would recommend the Day's Out ticket only if that exhibit is of interest to you. I love this tour and yes, it basically takes me 3/4 of a day to do.
This season the exhibit at Queen's Gallery is on Canaletto. (He is one of my favorites and I ~might~ have to make a special trip to London just to see this exhibit!)
https://www.royalcollection.org.uk/whatson/event/813258/Canaletto-&-the-Art-of-Venice
As you tour the State Rooms of Buckingham Palace there is an exhibition area there too and this year it will display Royal Gifts.
https://www.royalcollection.org.uk/collection/themes/exhibitions/royal-gifts/buckingham-palace
I also love to visit the Royal Mews. Usually in the summer there are only a few horses in residence. Last time I was there the docent was saying the horses have the summer off and get to spend it at Hampton Court! (And I asked at Hampton Court and no, they are not on view, lol!) Some of the Royal Coaches/cars are on display as well.