You'll need to log-in to your DJI account on the new phone, I guess the app you downloaded is much newer so perhaps some incompatibility with old firmware.
It should still connect though or you can't update?
However there is another way using the desktop/laptop based DJI assistant.

I wouldn't start trying to update firmware unless you have to.
I haven't updated anything in well over a year.
If you have a working system you can decline updates indefinitely.
Or stay more or less on the latest, either option has good/bad points.

DJi bring out new firmware every other week so if you fly infrequently the app is always nagging about something to do.
If you try to keep up, there is a consequent slight worry as to what has changed and is everything working properly on far too many flights.