Here is the banned bat list the list used by NFHS and USA softball
https://usa.asasoftball.com/e/BB1P2000.asp
The 52cor-300comp "pillow ball" is used primarily in slow pitch or senior series and honestly after an inning or two of play it dose not matter what bat you use thus why players call it the pillow or sock ball. Now ball performance does impact bat performance. Most sanctioning bodies use a 44/47cor 375 or 400 comp ball high seam or low seam so bat manufacturers use these balls for testing.
They will test the hotter balls as well as the pillow balls but the 52/275-350comp is the safety feature regardless of bat used.
As far as the bat, If you review the banned list you find some slow pitch models as well as fast pitch models that are banned for use in HS and USA /ASA play.
Now some other sanctioning bodies may allow these bats or, may have others on their list so it is important to check the list for your league/sanctioning body in which you play.
If a bat is not on the banned list for your league or sanctioning body it can be used as long as it has their stamp.
The major difference in slow pitch bats and fast pitch bats is length, weight, balanced, end load or max load.
Most females do not want a 26oz or heaver bat and most men do not want drop -10/12s so they will not market in both areas. The correct weight and length will be decided by the players size and strength and abilities.
With that said I have seen travel, college and HS ladies swing the slow pitch model 34" 26/27oz bat generally a single piece construction balanced. Some old school guys and ladies may remember before Bustos change to Demarini she swung a Miken Freak.
My DD swung a Freak FX700 max load 34/27and "ASA" Ultra II 34/26 in travel ball, HS and her first year of college before the team went to XENOs.and LS sponsorship. Then she swung the 34/26 or drop 8 Xeno.
During travel ball we were sponsored by Miken for 4 years so we got blems, demos and other products that wanted from them. We used them in all weather conditions, ball types even in the cages both SP/FP models. Even used the ones that survived after FP in SP leagues.