Well, the T1 to T4 speakers were the same with the same connections and were fully interchangeable, but won't work on any other keyboard.
The T5 ones are universal and will work with any keyboard. I have 1 pair left that I'm using for our PA5x display model (Korg's speaker bar just isn't that good, but it is compact). But they're no longer being made
And unfortunately, the GNSMS01 speakers will *not * work on T4. But T1-T5 speakers all will.
You *could* also just use a Yamaha Stagepas400 or 600 system. Or even a pair of HS8's if you aren't playing loudly (to all owners of HS8's, these are reference monitors not live monitors. Which means you can eventually blow them by using them at higher volumes or singing though them; you should never go into an HS series (or any reference monitors) with over 2/3 volume.
Yamaha DRX/DBX or Stagepas speaker systems are *live* sound reinforcement. Likewise JBL Eon's, QSC CP/K series, and Mackie SRM's (would all be designed for live sound use, but be aware the speakers with built in amplifiers I just mentioned are all rated around 1000w... so there is a very high noise floor if you tried using them in a studio environment! i.e. a ton of background hiss at low volumes.
Mark