Just like Lukas Prokop, I ran into an issue installing Vivado 2022.1 on Ubuntu 22.04. The error looks just like in their article: https://lukas-prokop.at/articles/2021-02-02-vivado-install-stuck
His article gives a recipe to fix 2018.1 version but it's not exactly fit for 2022.1, though an underlying issue is probably the same. Fix is very similar as well, and I'm trying to give more generalized approach.
The idea is to fix LD_LIBRARY_PATH environment varible for commands the installer runs.