Welcome to HA. Sorry about the previous post, sometimes we can be somewhat terse around here.
You most certainly can run HA over WiFi, I do, and have for years. No, it’s not “as good” as wired, and my preference would always have been a wired connection, based on past experience in the field. But I’m trying to get over that. Wireless networks are much better these days, and can be almost as reliable as wired.
That said, I don’t have any current instructions for setting it up. I asked this question back in early 2019 and was able to get enough hints to figure it out, but things may have changed since then. I did notice this link later that year and made a note of it then, maybe it’ll help. Even better would be to use a search engine with site:home-assistant.io and search this forum and the HA documentation.
Don’t give up, it can be done, and many of us are doing it.