No issues for me with a small exception that I also saw using Lightroom Classic but not Photoshop: first time I try to configure the settings in the print driver for Print Settings>Color Matching: the radio button what must be set for ColorSync was set for Epson Color Controls. That's not right! I quit (both LR and ACPU), tried again, then I saw the correct setting for the radio button (ColorSync). This isn't anything we end users can select, it is grayed out** by design.
I converted one of my Color Reference images to the output color space and saved it as a TIFF. Opened in ACPU, printed, it is fine. The GUI under 13.0.1 is not totally correct (some cut off) but it works. This is above and beyond the awful new GUI all print drivers are shown in Ventura.
So far, once the correct radio button is confirmed (and it seems now to be sticky but check), current versions of Photoshop, LR and ACPU seem to be fine.
**Some software products are using a private (undocumented) SPI called kPMApplicationColorMatching which you see in Photoshop and Lightroom and the Adobe Color Print Utility. When you set Application Manages Color, the area of the driver that controls Colorsync will alter the radio buttons such they are grayed out. X-Rite’s i1Profiler has also implemented this SPI.