8 Days in Madrid?

Traveling solo you can easily fit in a day trip to Segovia to see the Roman aquaduct and Toledo.

The Thyssen is supposed to be outstanding! We didn't have time to visit and I have always regretted that. I read somewhere that the collection consists of minor works by major artists and major works by minor artists.
https://www.museothyssen.org/

I also recommend visiting Retiro Park. Take your time to enjoy this lovely park, visit the Crystal Palace, and drink sangria by the man-made lake. Or take a rowboat ride.
https://www.esmadrid.com/informacion-turistica/parque-del-retiro

With 8 days in Madrid, would you consider spending a night or two in Toledo? Toledo is lovely but very crowded during the day with tour buses. In the evening it's so much more pleasant when the daytrippers have left and the city is illuminated.

You have time for one night in Toledo, which would give you time to explore with fewer others around. It's an easy train ride from Madrid, and could be a day trip if you prefer. Segovia would be another good day trip. I agree that Cordoba deserves more time, but you could get there, see the Mezquita, and return in a day if necessary. The Mezquita is a unique combination of Moorish and Gothic architecture. I liked the Thyssen Museum, and I thought the National Archeological Museum was excellent.

So, a day at the Prado, a day for the Royal Palace and perhaps the Reina Sofia, a day for the Thyssen, Retiro Park, and Archeological Museum, two days to Toledo and back, a day for Segovia, and a day for Cordoba = seven days. Maybe that's "spreading too thin," it would certainly tire me out, but it's a good menu to pick from in any order. Make Toledo just one day and take a day in Madrid to recharge, do laundry, sit in some cafes and tapas bars. You'll enjoy Madrid.

EDIT -- If you like Spain, you'll love Andalucia, and you could put off Cordoba till that trip. It's the hub for the train lines that connect Madrid, Sevilla, and Granada, so easily visited if/when you return.

last year i spent 6 days in madrid. while I loved the prado, the reina sofia, and the thyssen bozmazia I didn't care for the city per se. my taste has shifted more towards smaller/medieval stone and brick towns and villages and away from neoclassical. loved teledo and segovia. on hindsight, i should have stayed at least one full day in each and cut a few days out of Madrid. if you love art toledo with its multiple el greco's is a must-see. segovia's amazing aqueduct is not the only site in town. multiple romanesque churches rival those in italy. along with teruel segovia is my favorite spanish location so far. this year i am going to visit caceres and avila, perhaps medira on my trip through western and northern spain. as others have said cordoba and granada are best left to another trip.

I will also be in Madrid early May, and take notes.

May 1 and 2 are holidays in Madrid. Be aware of closures.
https://www.citylifemadrid.com/public-holidays-in-madrid/

Festivals:
https://www.madrid.org/fiestasdel2demayo/2023/index.html
https://www.spain.info/en/calendar/festivals-dos-mayo-mostoles/

https://www.esmadrid.com/en/whats-on/sanisidro-madrid

If I were you, given what you've shared about your interests, I'd definitely take a train to Granada to see the Alhambra. Art, history and architecture are there combined in a way seldom available elsewhere. Although the train will take 3-1/2 hours, IMO it's well worth it.

Don't forget the scenic Salamanca. I stayed there for 1-2 nights while traveling in Madrid.

Since you love art, history and architecture, you are in for a treat no matter what you do both in Madrid and in Rome! How wonderful.

I endorse the recommendations for Toledo and want to add: it's an easy short train ride. It leaves from Madrid Atocha station which is close to many of the museums you want to see so I assume you may be choosing a hotel located nearby. Atocha station has a lovely indoor palm tree garden that is very refreshing to wander in while you wait for your train. Give yourself plenty of time for your train as there is a bit of a process to find and pass through the gates.

The station in Toledo is gobsmackingly gorgeous and I wasn't prepared for it. The elevators to take up to Toledo's old town on top of the hill are a godsend in the heat! We took a taxi from the station to the elevator. This will help keep your energy up.

On Twitter I follow Dr Peter Paul Rubens, @pp_Rubens, an account that features works form a different Dutch Golden Age artist every day, plus many from other countries in the same time period. I have learned so much from this account and cherish it! He just featured El Greco and showed many paintings set in Toledo 400 years ago. You might enjoy looking at his recent postings on Twitter.... since they feature art, history and architecture in a location you will hopefully soon be visiting!