I lean in the same direction. It's Serena, Graf, and Martina for me as well. The focus on slam counts only just became a thing over the past two decades. Just as Emerson wasn't considered the greatest despite holding the slam record prior to Sampras taking it, Court wasn't quite considered the greatest despite the 24 slams. Nobody in tennis thought Emerson was a better player than Laver or Borg, for instance.
Regarding the GOAT debate in women's tennis, Serena has a strong claim because she has 23 slams and an argument can be made that the athleticism of the sport is higher than it was 3 or 4 decades ago. But I - like you - don't think it's that simple.
Steffi won 22 slams in 12 years compared to Serena's 23 in 23 years while playing against stronger competition, such as Navratilova. She won the Golden Slam in 1988 which eclipses anything Serena has every done, and has double the career grand slams that Serena does. Peak for peak, Steffi was simply more dominant, winning 6 consecutive slams at her best. She also has Serena comfortable beat as far as weeks at number 1 go.
Navratilova has a staggering 59 grand slams (!) in total (singles, doubles, and mixed) and is 2nd all time to Graff in weeks at number 1. And would have won a lot more slams had she not had the misfortune of having to come up against Evert and Graf.