I am quite sure the R6 shipped with the 1.1.0 update, mine came from the store with it anyways. Maybe the R6's 1.1.0 is different than the R5's, not sure. Canon is very confusing on this, as they don't talk about 1.1.0 on the R6 or have it listed as a previous version, etc. However they have been shipped with that version.
I wonder if Canon quietly updated R6s with the new 1.1.0 firmware so that they didn't continue to have an onslaught of overheating vlogs. The R6s weren't available for almost a month after the R5. However some folks received their R6 with version 1.0.0, and they aren't able to upgrade the firmware to 1.1.0, so again this is very puzzling, as to why Canon did this update secretly on some and didn't make the firmware available to the rest of the world.
Version 1.1.1 has these following release notes, at least for the R5, so it's not a big update unless you have a 100-500.
Firmware (Version 1.1.1) incorporates the following improvements and fixes:
When the RF100-500mm F4.5-7.1 L IS USM is attached, image stabilization of 6.0 steps is now possible when used in conjunction with the optical image stabilization mechanism of a compatible lens.
When the RF100-500mm F4.5-7.1 L IS USM is attached, the IS performance during continuous shooting may deteriorate with firmware Version 1.1.0. This phenomenon has been corrected.