I failed to replace my chain at the proper interval. Will I have to replace my whole drivetrain?
Yes - after that mileage you will need both a new chain and new cassette.
A new chain on the old cassette will not mesh right, and accelerate wear on the new chain.
Depending how much chain elongation has accrued, you may need new chainrings too.  They wear slower because more teeth are engaged in the chain.  Look at the chainring and see if the scallops are asymmetric, which is worn.  You can also wrap the new chain around the teeth firmly, and look for gaps between chain and chainring.
There's also a chance you may need new jockey wheels in the derailleur, though these are only guides and not load bearing so tend to last a very long time.
It would not hurt to replace the gear cables too - they're a relatively minor cost, and a complete fresh set will make it all feel even better.   You should also deep-clean both derailleurs, and lube the shifters while its all apart.