Spoiler: you will come to the conclusion that you can’t find the additional bits. Your only option is to break compatibility and create a new packet header format. At this point you can choose literally any size address larger than 32 bits. 64 is good, but the cost to go to 128 is literally nothing while giving you a lot more possibilities of what you can do with it.
Lastly, IPv6 fixes a lot of craft from IPv4. It is a more streamlined protocol that is actually easier to work with than IPv4. The people who told you that IPv6 is overengineered didn’t have an alternative better protocol. Their point was that IPv4 is fine and we don’t need anything but what it provides because a new protocol is scary and annoying to learn because new things are scary. Literally, mathematically, there is no alternative that solves address exhaustion in a backwards compatible way. CGNAT is the overengineered hack, not IPv6.
I really hope you stop respond in to people with nonsense before you look at the packet structure yourself.