I don't install anything to C, let alone Program Files. As a general rule of thumb, last time I knew, that was the first thing to avoid when modding (ie avoid putting games and mods and modding tools to protected directories).
This is a bad rule.
It's probably advice given for Morrowind, 15 years ago by people who didn't know better at the time and since then people follow it like it's been brought down from a mountain on a stone tablet.
But it's not a good idea today, this problem is testament to that.
Vortex is a standard conformant windows application, using a standard installer with default settings. It behaves like 95% of Windows applications out there, yet people manage to screw up their install and delete their data by using non-default install locations and manually changing their settings.
At that point you should ask yourself if maybe your "house rules" are standing in your way more than they help you.
The reason people may have advised you to avoid putting modding tools into "program files" is because those modding tools tried to write files (logs, mods, ...) to their installation directory. Vortex doesn't do that, so the advise doesn't apply.
The reason people may have advised you to avoid putting games into "program files" is because otherwise the write protection would prevent you from putting mods in there. But you could just as well disable the write protection punctually for the data directory. This is less work and more secure.
And most of the time you don't even have to do that because Steam (by default afaik) already allows writing to all game directories. So again, this advise doesn't apply for most games today.