Few points:
1. You don’t need ProRES or even LOG for 99% of footage, since you will need to waste time editing that mess;
2. H264 is just FINE. Has many bitrate options in 3rd party apps, white balance fine tuning, so you will rarely need to go ProRES at all;
3. You can write to SSD I guess, which is the best option;
4. Some new phones have unconfirmed lens focusing issues, so if you are lucky and don’t have that - do not risk replacing phone. People on this forum have tried multiple phones just to get rid of this seemingly hardware problem. If your current phone works - leave it as is;
5. 256GB is already A LOT. I used to shoot beautiful videos on my 16GB iPhone 5, I still rewatch these videos and they look gorgeous. Would have never thought I might need 4K or LOG or ProRES back then, and don’t think I need it now as well. Only recently moved on to 4K after all my main devices started to support it, as well as I got myself a great fast SSD to store that;
6. Storage. You will need to store that footage, back it up, archive. You know, it might get complicated faster than you think. And apps like Handbrake won’t always help and are not really efficient storage-wise;
7. 512 is not much larger for storing ProRES. Also editing these videos on your phone is not the best solution, you are better with copying them to Mac and finishing them off there, so not much difference in internal storage sizes;
Verdict? Get a decent SSD instead.
UPD: you upgraded. Well, good for you, might be a better option if you like rewatching photos and videos on your phone instead of making copies more often