At least on a VI, select camera2 menu, page 9/10, is labeled "Custom Operation1"
First item is picture custom key (next two items are movie symbol and play symbol custom key). choose that, and it lets you assign custom functions to each of the buttons around the control wheel when you are in picture mode.
I think the one with the trash button (C button) is probably the most disposable, because there's no logical function associated with a trash bin when in shooting mode (whereas left and right on the control wheel have timer/multishot, and flash modes respectively), and with mine (bought used so I'm not sure if it comes that way default or was assigned by the prior user) it was set to ISO, to instantly get you to the ISO settings.
So if you click on menu for C button, then it gives you choices on what to assign to that button.
On page 3/20 "AF1" for possible assignments, you have
Focus mode (if you want to cycle through AFS, AFC, etc options),
AF/MF control hold (which basically makes it MF as long as you hold that button), or
AF/MF toggle (which is most like the AF/MF switches on some DSLRs, flipping to one mode or the other until pressed again).
I think the 3rd is probably the best unless you are good at double presses (holding the C/trash while pressing shutter), and you want to re-select the snap focus point between shots often. If you're apt to forget you left it in MF mode then you might opt for the 2nd, because once you release the C button you're back into AF mode so if suddenly something happens at a much different focus point you're back to normal operation and you don't miss that shot stuck in MF at your previous target focus distance.
So decide which you prefer.
Having to combo press the C then shutter to take a shot kept at your last half shutter focus point, but being ready to resume AF the instant you shutter without holding C?'
Or toggling AF/MF and possibly being caught in MF mode in the instance you forgot to switch back and have a subject at a vastly different focus point?
Interesting, can you describe this a bit more in detail?
I do not make a lot of "street" photos, but I certainly understand the need for being able to set a fixed focus distance so you can shoot without looking in a viewfinder or on a screen. I find it useful when I want to be very discrete and also when the light conditions make screen (and on my RX100m6 sometimes also EVF) use difficult. It decreases the need for exact framing. I use AF to focus anything at the chosen distance (half-pressing the shutter button) and then change to manual focus. I have set up the left rocker to toggle between AF and MF. It is not quite back-button focus, but it works well, and is similar to what I did with analog cameras a couple of decades ago.