Unable to install watchOS Device Support for Watch3,2 8.7.1 (19U67)

I was getting an error from Xcode (14.3, 14E222b) when connecting my Apple Watch to the system Watch3,2 running 8.7.1 (19U67). The error is:

The device is not available because there is an error downloading the symbols.

I was able to download the symbols manually, from Apple's CDN: https://devimages-cdn.apple.com/downloads/xcode/dsc/Watch3_2_19U67.dmg , but when trying to install on MacOS Ventura 13.3.1 (a) (22E772610a), I get an error from the installer:

This package is incompatible with this version of macOS. The package is trying to install content to the system volume. Contact the software manufacturer for assistance.

How can I fix this issue? Why would I not be able to install the debug symbols for this OS? Do I need to downgrade my OS to be able to develop for this watch?

Thanks.