Hope so - Users are reporting that the update to macOS 11.6.5 fixes the print issues.
There is apparently a bug in macOS Big Sur 11.6.2 in connection with ICC profile use/printing,
Some users have reported success after updating to macOS Monterey, personally, I'd be more likely to go back a version rather than jumping into a new macOSversion so soon after release.
Sadly this bug appeared to still be present in macOS 11.6.3, according to users here who have made that upgrade.
Some users have reported positive results in macOS Big Sur - with some profiles being usable after opening them into the ColorSync utility and “fixing” any errors found.
macOS Monterey Problems with printing using Photoshop manages Color?
Users have reported a bug in macOS Monterey 12.2.1 in connection with ICC profile use/printing,
[as there was with macOS Big Sur 11.6.x, fixed in 11.6.5]
It’s been reported that the macOS Monterey 12.3 update fixes the issue.
You also mention missing Epson's standard profiles, they are hidden, see below :
Epson printer profiles are missing in Photoshop manages color in the print dialog (Mac)
To use "Photoshop Manages Color" properly (to make accurate prints) you need access to the printer manufacturer's paper specific profiles, since you need to select the relevant paper profile in that dialog.
Using "Printer Manages Color" should work for Epson’s own papers, as long as the printer driver is correctly installed.
Printer Manages Color [based on the media type selected] calls upon ICC printer profiles from a different installed folder*
[*usually a hidden one, this is so they don't get deleted inadvertently, more on that and how to find them below].
Epson ICC printer profiles may be missing in Photoshop after updating macOSX. This issue started with Mojave.
There is the actual filename such as "MyPrinterPaperProfile.icc" and then there is the internal name of the ICC profile that is displayed inside software, such as "My Unexpectedly Different Profile Name for the Same Printer and Paper" which may be throwing you off? Another thing is that you may think that this is a CMYK profile when it is RGB, so it may not be visible where you expect it to be?