From some deep diving, synthetic change dates
1997 - Broncos, Bulldogs, Raiders, Sharks, Cowboys, Panthers (Nike/Super League)
1999 -
Manly (Classic to FILA)
* Penrith reverted to cotton (Nike to Classic)
2000 - Newcastle (Classic to FILA)
2001 - Parra (stayed with Classic), Roosters (Classic to Kappa)
2002 - Souths (were with Classic before removal in 1999, returned with ISC)
2004 - Penrith (Classic to ISC)
2006 - St Geo Illa was in 2006 switching from Classic to adidas
Warriors (1995), Storm (1998), Wests Tigers (2000) and obviously the Titans (2007) and Dolphins (2023) have always been polyester. Northern Eagles (2000) were synthetic all three of their seasons.
As
@GAZF said above, NSW (2007) and QLD (2009) held out a fair bit longer before changing. From what I can deduce, Australia's jersey didn't go synthetic til 2010.