Can’t install steam?

Got an old Mac book air (2017) running on High Sierra (not enough space to even update it, even after deleting everything apparently) and I’m trying to reinstall steam. I had it before and deleted it ages ago. Now I’m trying to reinstall it and when trying to run the installer I got from Steams website it says “steam.dmg” is damaged and can’t be opened. You should move it to the trash.” From online searches I suspect it’s something to do with some of the old files remaining from when I had it before, but what sort of messed ups design is that? Anyways, I’ve gone through the cache, logs, and application support folders and removed anything that says steam/valve in the file/folder name. I found a few and they’re all gone now along with some old game folders I found. I’m at my wits end with this and am really hoping someone here could provide some advice other than completely wiping everything and starting from scratch.