Cannot use 4G/5G on Fairphone

I can reproduce this seen as a toast bottom of screen. When Wi-Fi is off like this what shows as a connection icon in top right status bar? (This Settings location changed @Jets in a15.)

Your APN may not be exactly correct.

Settings > use Search facility > Access point names. Compare with your carrier published APN.

Preferred network type can be worth adjusting. Do you expect good 5G? If not try 4G. For 4G use something like LTE/GSM/WCDMA but not NR.

I think I wasted time by swapping these too fast.

Most unlikely.

Edit in testing I suggest you have all Advanced Privacy turned off.

“Looks like” ?? FP6 mobile data connection shows no internet connection