Here is a list of the 81 new style names I found that are on the SX900 keyboard

Ballroom - 1
Cha-Cha

Dance - 10
70sSpanish Disco
90sPopBallad
CassicalPop
ClubMixDJ
ClubPeffaeton
DiscoSurvival
FrenchDJ
MinimalElectro
NatureHipHop
RetroSoul

Entertainer - none

Jazz - 5
BigBandSwing
CoolJazzWaltz
CoolSwing
Easy8Beat
FastJazz

Latin - 9
80sBrazilianPop
CoolBossa
CubanCha-Cha
EuroPopMambo
FastCha-Cha
PopBachata
Reggaeton1
Reggaeton2
SalsaGranCiclon

Movie&Show - 5
BlockbusterBallad
Gunslinger
IcyBallad
OrchMovieBallad
PopMusical

Pop&Rock - 28
6-8BalladRock
6-8ChartBallad
6-8GuitarBallad
12-8PopBallad
16BearRock
90sAussiePop
90sDancePop
90sUS ChartBallad
CanadianTeenPop
ContempGtrPop
CountryBeat
CountryPopDuo
CrazyPop
DancehallPop
ElectroRock
GrungeRock
IrishPopRock
OrchRockBallad1
OrchRockBallad2
ReggaetonSlowJam
RockShuffleFast
UK FolkPop
UK SoftRock
US CountryPop
US ElectroPop
US FolkPop
US singerPop

R&B -4
60sBigHit
JustRnB
R&B SlowBallad
UK Soul

World - 19
ArabicEuro
Bhajan
Bhangra
Duranguense
Grupera
ZitherPolka
Jing Ju Jie Zou
Keroncong
Laff
MalfulFunk
ModCeltic4-4
ModCeltic6-8
ModernDangut1
ModernDangut2
Saeidy
SaeidyPop
US MarchingBand
WehdaSaphira
Xi Qing Luo Gu

note: courtesy of Drake on Psr tutorial forum

The exact number most likely depends of what model it's compared to.

At PSR Tut there is stylelists and info for different Yamaha models:
https://www.psrtutorial.com/sty/yamaha/index.html

In addition Yamaha keeps changing names of the same styles.
There will be probably far less than what it looks like.
Compared to the S975 a lot more styles
Compared to the Genos only a handful.
They are available for download on the PSR Tutorial site.
I did audition most of them ....
Eric