Update on this.
One user I found out seems to have a known "problem child" system and always needs special attention for downloads, etc. The 2023 change over install took 3 attempts before it completed. As far as his Vault Client, yes, they left the 2018 version on everyone's systems. Once 2018 was uninstalled and 2023 reinstalled, all seems to be working fine. IT wasn't aware best practices are to uninstall the older releases, especially Vault Client prior to the new install.
So, IT is now planning on doing an uninstall of 2018 apps, leaving a few specific stations with such still available just in case (without the Vault Client), and then repair or reinstalling Vault Client 2023 to fix this issue.
We also found a very similar error and were able to fix that by having the user log out of their Adesk account, reboot and manually log back into the Adesk account.
So things here are finally looking up. Considering they went into this large jump update kinda blind, it went fairly smooth and only a handful of issues. Some are, of course operator error and bad practices. But that's why they brought the Angry Elf in to clear up...;)
Thanks everyone for your help!