Itinerary Critiques/Suggestions?

Bus is the logical option from Donostia/San Sebastián to Bilbao, not the train. Spain offers a very wide variety of climates, the north is rainy and cool (think of Seattle weather).

You didn't mention my two favorite places in Spain:
Seville and Toledo

Toledo was the capital of Castile and Spain 500 years ago when it was moved to Madrid. It is special, you can do a day trip from Madrid, but expect to spend a full day there.

Segovia is another city close to Madrid that deserves a day trip. It has an intact 1800 year old Roman aqueduct.
I suggest you could cut one day from Barcelona, another day from Granada and another from Madrid. Spend three days in Seville.
Also, if you want to see Cordoba, do it when traveling from Seville to Madrid.

From Barcelona consider a day trip on the train to Monserrat. Go early

Thanks Mikel for the suggestion on buses from San Sebastián to Bilbao. Looking into it, the train takes quite a bit longer to go from city-to-city, in comparison with the bus.

Thanks geovagriffith for the suggestions on Toledo and Seville, and other areas. I had considered adding Seville, since I would already be in Andalucía for Granada. Would 3 full days be enough for Madrid and Barcelona?

I also wasn't aware of the aqueduct in Segovia. That sounds so cool!

So much to see, so little time!

I'd take the train from Granada to Madrid. The trip is under 4 hours, you go from city center to city center and the basic fare if you buy early and get the discount, is €35.50. When you add the time and cost to travel to/from airports plus the additional lead time at the airport, flying probably won't save you time or money and the trains are comfortable. The official site for schedules and tickets

I would not eliminate Granada. There's a reason the Alhambra is the #1 tourist sight in Spain. Make sure to buy your Alhambra ticket before you commit to stay there. Tickets always sell out. Official site

You haven't told us what you want to see and do, what your main interests are. So it's hard to advise on your time allocation. I love Barcelona and haven't run out of things to see and do in several visits totaling more than 2 weeks. It has some fine beaches, beautiful old churches, lots of art nouveau design and architecture, Gaudi creations, millennia of history, and excellent art museums and even a hash (hemp) museum. And lots of sports activities and day trips. Madrid, OTOH, is not a very interesting European capital. It has great art museums, but unless you want to spend 2 full days looking at European painting, 4 full days is a lot . Instead of a day trip to Toledo, I'd recommend 2 nights there. The city's easily overwhelmed by daytrippers but is magical in the early morning and evening hours (and added bonus - the temps are lower then), when most of the tourists leave. There's no discount for early purchase but you should buy a few days in advance as they often sell out.

There are so many ways to organize a first trip to Spain. This is a pretty good plan - especially for a solo guy your age. Depending on interests you can consider the following:

There are a ton of great day trips from Madrid -my first trip to Spain was in my 20s and I spent a chunk of time checking out at the areas around Madrid - Segovia and Toledo were mentioned but there are several other sites of interest.

I love Granada and southern Spain -but if you’re looking to manage travel fatigue and costs perhaps focus your trip in the central / northern areas. If you do keep Granada in your plan then dropping a day from Barcelona and Madrid to add Sevilla and/ or cordoba are great suggestions - but as you noted August is hot.

With jet fuel shortages I would avoid flights in country as I think those flights are likely to be cancelled. Train would be a better option. Also overnight trains are a good way to travel on a budget - and you’re the right age for that!