Are shoes very important for running?

I've recently gotten into exercising and have been doing cardio by running 5–10km every day. I've replaced everything with high-quality gear—tops, bottoms, wrist guards, patella straps, waist belts, etc.—except for my shoes.
I've been alternating between some Adidas sneakers that cost less than 100,000 KRW and some Asics velcro sneakers for daily use that cost in the mid-100,000 KRW range, but I'm starting to get interested in proper running shoes.
I'm looking into the Nike Vomero Plus and Hoka sneakers; it wouldn't be a bad idea to invest in a proper pair of running shoes, right?