What kinds of objects were you trying to focus on, and how far away were they?
Is it always the same objects with different cameras?
"people 15 to 50 ft away."
Perhaps not the best for testing AF.
Very first top of the list. Reset the 5D Mk III, great camera BTW, to factory default. There is a possibility you have set something off. Clear all settings and, important, clear all custom settings. Makes sure all the lens switches are in their default positions too. Any AF lens needs vertical lines and contrast to focus the best. After reset try using AF with the problem lens on some things with good contrast and some vertical lines. If it now works, it works and there is nothing wrong with it. If it doesn't it needs to go back to Canon and tell them how you tested it.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM