Just back - not my first trip to Edinburgh, but first in over a decade. I'll summarize my thoughts after seeing many of your spots of interest. I do agree with the well-articulated thoughts above!
Arthur's Seat - this is more fun as a minimum half day (in my opinion). It's a long, even if striking, hike. More time consuming than might be worth the over-view for you with only a day and many other places to see. Taxi up and down?? Calton Hill - less time, but is a quick over view more valuable to you than spending time at one of the other venues? Only you will know - and, of course, inclement weather may help your decision!
New Town Walk and/or Royal Mile Walk - Probably not time for both if you want to make some of your other stops. As suggested above, Royal Mile would be my priority.
National Gallery of Scotland. I "reviewed" my experience here, scroll down:
https://community.ricksteves.com/travel-forum/england/itinerary-feedback-please-edinburgh-york-cotswold-london
Summarizing - do your research and ask directions to the gallery(ies) you want to see. Sadly, I found my multiple hours there quite disappointing due to curation that I felt could use improvement. (I felt somewhat vindicated, although no less disappointed, after reading reviews from others who felt similarly.)
Holyrood Palace - this was my reason for including Edinburgh in last month's quick UK trip. I had always missed it on previous trips. The Palace didn't disappoint - read up a bit on Mary Queen of Scots and Darnley before you travel (if you aren't familiar with their "story"). Are there "tours"? I had a standard audio guide which was sufficient. You can move at your own pace. Obviously, Holyrood was a priority for me and I'm very glad I finally made it!
St Giles Cathedral - could be a quick stop along Royal Mile. Many include a walk through on their Royal Mile explorations. If you do stop in, The The Thistle Chapel is worth seeing - Order of Chivalry with long history. https://www.stgilescathedral.org.uk/the-thistle-chapel
Gladstone's Land - I had expected to enjoy this more. Staff in each room to explain the era and situation depicted, but somehow, maybe I didn't ask the right questions, but I didn't walk away feeling I'd learned anything. I enjoyed John Knox's House more. There, I did feel that I'd learned something of his experiences and times.
Castle - didn't visit inside this trip. I still remember being underwhelmed from a first visit many years ago.
National Library - not up to the Treasures at the British Library in London (if that is the level of expectation). I ran (literally) to see the exhibits on my final day in town before heading to the airport and am regretting to this day that I made the (rather strenuous) effort. There is currently an OK exhibit on R. L. Stevenson and his time in Samoa - but if you've read the recent book "A Wilder Shore: The Romantic Odyssey of Fanny and Robert Louis Stevenson" by Camille Peri, there wasn't anything new.
Just to give you some time reference - I had about 3.5 - 4 hours for a Royal Mile walk with stops including Writer's Museum, Gladstone's Land, John Knox House, Museum of Childhood, People's Story, and a quick run through Museum of Edinburgh. All of the museums are small, several free. I was watching the clock! Of these, I most enjoyed the People's Story, John Knox, and the Museum of Childhood (surprised me there). It does sound as if you have researched the stops that might be of most personal interest - my only thought is be open to changing to your mind if something doesn't hold your interest as expected.
Good luck - as you know, one day will just be a teaser for a return visit!!
edit - cross-post before your above reply. I'll leave my thoughts as they stand, even though you've addressed some of my "meanderings"