The entry subscription only comes with the first two expansions (ARR and Heavensward) and 30 days of game time.
If your jobs don't level beyond lvl 60 it means you don't have the Stormblood, Shadowbringers and Endwalker expansion which are required to raise the level cap on your end. It doesn't matter that you're paying the regular sub because you're still missing the necessary expansions.
What you need to do is buy Endwalker on their online store. You only need to buy Endwalker because whenever you buy the newest expansion it also comes with all the previous expansions (minus ARR and HW).