Catapult can and likely will be procured from abroad.
Frigate and destroyer level capability isn't a technological barrier, bigger missiles and arrays aren't some magic tech - especially in Indian case, where those are procured from abroad.
It's a matter of being able to afford connectivity. Before 2020s, India couldn't; it's but another case of realistic assessment of own capabilities. In 20300s, b/c of changes in space sector(affordable connectivity) and indian economy, it's going to change.
Also, average modern indian frigate/destroyer AA(barak-8 with elta aesa setup, or shtil+barak-1), while shorter ranged than small minority of HHQ-16F-equipled 054A(last batch), is higher than most Chinese frigates with the exception of 054B; at worst, similar(11356).
Chinese "corvettes"(light frigates) carry only HHQ-10, i.e. a self defense suit.