What is the best camera app for iPhone 15 Pro Max to shoot in 4K @ 24FPS with quick file offloading?

Yes. I would suggest doing a lot of testing before actually shooting.

Just to clarify a couple of things as well. If the OP is using ProRes, you can record ProRes internally at up to 30fps using the FCP app so there is no need to have an external drive attached while recording. Here is a link to the official Apple guidance on ProRes requirements:

About Apple ProRes on iPhone – Apple Support (UK)

The reason I strongly suggest Apple Log is that it allows for a lot more flexibility in post. The HDR (HLG) mode does an awful lot of processing in the phone which is burnt into the footage. It looks fine on the phone but when you see it on a big screen it looks very over-processed. Apple Log as with all log takes a bit of extra processing but looks way more natural and FCP does a very good job on it. There is now a LUT in the FCP app that allows you to preview Apple Log as HDR or SDR when shooting which is very useful.

The speed of loading the files is limited by the connection between your iPhone and your mac.

Using, for example, Blackmagic Camera on your iPhone (a pretty nice camera app, and free...), you can record directly to an external SSD, and I expect that if you then import from there instead of the iPhone storage, it's probably faster.

As I understood your question, you wanted to speed up file transfer.

There are two ways to achieve this: smaller files, or a faster throughput.

For the first, recording in H265 (a.k.a. HEVC) typically produces smaller files than H264 (and MUCH smaller than ProRes).

For the second, a fastish external SSD can transfer at maybe 1000MBps (there are faster than that, but it would be overkill).

Older models of iPhone were very limited by the Lightning interface (basically transferring at USB2 speeds, twenty times slower or so).

The iPhone 15 Pro has USB-C, but you need a proper USB-C data cable to make use of the available speed.

The charging cable that comes with the iPhone is limited to USB2 speed.

You are making this way more difficult than it needs to be. All of the main video apps can record internally at 4K 24fps on the iPhone 15 Pro Max (ProRes or HEVC). Choose your app and record. You don't need to record externally. To get the footage off the phone, plug in an external SSD of your choice and use the Files app as I have already told you in your other thread. That is the fastest way to do this and you don't need to have an SSD plugged in when recording. You can use the FCP app or CinemaP3 (the best IMO as I said in the other thread). I'll leave you to it. Best of luck.

And use Apple Log, not HDR or SDR.

In addition to what Clint said: you should not make a decision on frame rate based on “saving space”.

I would recommend that you do a dry run before you do actual filming. If you are concerned with space, then probably ProRes is not the choice. Try filming in ProRes snd HEVC and compare.