The virtual work visa isn't actually available yet.
If you are recently out of university, you can get an H-1 visa.
car ownership
Well, you won't want that in Seoul.
Should I get a visa sponsorship for my employer,
If your employer is a not a SK registered employer, how do you expect them to sponsor you?
the easiest way will be for u to get an official visa.
from all the places i've been a DN, korea is one of the ones that is toughest as a DN.
for example, u can't use the biggest food delivery app, you can't use coupang (equivalent of amazon), you couldnt use the taxi app (now uber is available so it's fine), etc.
You can use kakaotaxi as a foreign visitor (used it myself with cash I think although it's a hassle to get it working)
I need a starting point
Marry a local.
PR requires residency which can come in the form of local job or study and you have neither of those.
A resource recommendation - the people behind the channel The Suitcase Designer on YouTube have stayed in Korea for several years (as American citizens), and are doing so at the moment on tourist visas. I imagine some of their past videos might be helpful resources to see how they got the right approvals.