How much storage do I need for my iPhone usage?

If you can afford more memory, buy more memory. Especially, if you buy an iPhone 16 Model, which will have Apple Intelligence, which will use more memory than an iPhone without Apple Intelligence. Keep in mind that once purchased there is no way to add memory to an iPhone.

This thread seems to be conflating two things: RAM ("memory") and storage.

Apple does not make a point of advertising the amount of memory (RAM) on IPhones, but information is available (e.g., from MacTracker). This is relevant to questions like "Which iPhones will get Apple Intelligence?" - and also might be one predictor of which iPhones will best run a new iOS release. (I believe only one or two of the iPhones that can run iOS 18 have as little as 3 GB of RAM, whereas all of those that initially shipped with it have 8 GB.)

Storage retains its contents after power goes off. No iPhone to date has > 8 GB of RAM, but there are a number of iPhones that have 128 GB of storage. These days, that's a fairly low amount, but I suppose that if one did not have lots of photos / videos, music, movies, TV shows, etc., 128 GB could be more than enough.

Probably, but I have yet to meet the first person who ever regretted buying too much memory.

Because the processing will be done directly on your iPhone. It's not like a link to ChatGPT. It's on device processing and one reason the ONLY iPhones which can even get Apple Intelligence are ones with 8GB of RAM, which is iPhone 15 Pro/15 Pro Max and all iPhone 16 models. All other iPhones won't get Apple Intelligence as they don't have the processing power to use it.