I love the 7th and find that where I stay it's not particularly crowded.
When I was in Paris in October I found the Orsay, Louvre and Orangerie were terribly crowded. In fact, due to crowding in the Orangerie I skipped the Waterlilies on the entrance level and headed downstairs where it was literally shoulder to shoulder in what previously would have been fairly empty rooms.
I did find the Cluny fairly empty but the day I went about half of it was closed. I think it was due to staffing issues but they were not real clear on that. The room with the Lady and the Unicorn tapestries was open which is always my target there. I actually had the room to myself a few times out of maybe 15 minutes. I could easily sit on the bench area and look my fill without feeling like I needed to move on.
I also went to Basilica Saint-Denis on the north end of town. It's an outstanding example of Gothic architecture. I'd been there a number of times and it is never crowded and this day proved no exception. I got myself tangled up on museum closures and wound up on a Monday without a plan in place and all my museum choices booked, so headed up there. It was perfect. There were a few school groups there ranging from what looked like university aged students to little ones holding hands but it did not feel crowded even in the crypt.
I finally made it to the Museum of Hunting and Nature which has been on my "to-do" list for years. It was surprisingly crowded. There was a new exhibition opening and it was school break so lots of families were visiting as well as folks who were clearly there just to see the exhibition. I thought this museum was interesting and perhaps it will not be as crowded next time I drop by.
The Louvre is always crowded along the trail to the Italian paintings section and the Mona Lisa but if that is not on your list of things to see then there are areas where it is relatively uncrowded. You have to be determined to get thru the scrum under the pyramide but I always stop by to see the Vase of Alienor d'Aquitaine in the Richelieu wing as well as the rooms with the Vermeers and Rembrandts one floor up. Also on the top floor of the Sully wing are, perhaps surprisingly, a room of Impressionist paintings including a few by Monet and Degas. Here is a link to gallery closures so you can decide what you want to see on your visit.
https://www.louvre.fr/en/visit/list-of-available-galleries
Although I did not go this last trip, my prior trip in 2023 I did the Quai Branley Museum which was deserted. Haven't been to the Guimet in a number of years so not sure if it's picked up crowds or not. I also enjoy the Museum of the Resistance and Liberation which is across the street from the entry to the Catacombs and is free but did not go this last time. Army Museum is usually relatively uncrowded and it may be very convenient to where you are staying in the 7th but it depends on if you are interested in military history or not.
I visited the Petit Palais in October as well. It's a free City of Paris museum, charging only for their special exhibitions which are wonderful. I was shocked at the crowds at this museum as well. Every other time I've been there it's been pretty sparsely visited but wowser. The special exhibition was jammed (Swedish artist) as well as many visiting the free galleries.
Have a wonderful time!