Excellent points about cables, including the part about the cable needing to be able to xfer data.
While the cable I'm currently using is made by Apple, it is about 6' long, and has a smooth surface.
I have at least one Apple MLL82AM/A "240W USB-C Charge Cable (2 m) … charge cable is made with a woven design … ideal for charging, syncing, and transferring data … It supports charging of up to 240 watts and transfers data at USB 2 rates." I will get that cable from its current remote location and try. I'll also try different USB 2 ports on my MacBook Pro: 14" M3 Pro. I have three ports on my computer that accept USB 2 cables:
From: "System Information":

I don't know if the three busses are equal in capabilities/specs.
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All that said, I did some testing:
When I connect my phone and enter my iPhone password (to trust my computer), the macOS Finder window for the iPhone sometimes/often displays and comes to the foreground (in any case, the iPhone shows as mounted). I usually switch to a different app, (but don't close that Finder window). Today, I kept the iPhone Finder window in focus (active, with all other apps/windows in the background). I watched a backup complete successfully, and verified that by checking: "Manage Backups…". The fact that I kept the iPhone Finder window in focus most likely has no bearing on anything (because a backup should not require that), but I thought I'd mention it.
I did not get any subsequent request to enter my passcode. This could be purely coincidental. I'll keep an eye out on things.
Question: If you connect (via USB) your iPhone to your Mac and a backup is performed, if you leave your iPhone physically connected, will you be prompted to make subsequent backup(s)?