There are some prerequisites that that site doesn’t satisfy to have that feature enabled. Pro level account would have been the big one, but indeed, I can see you’re there. Here’s what ELSE must also be true:
domain aliases won’t work (those may all be covered by the wildcard, though, so I can remove them while configuring the site if you take care of #1
branch subdomains won’t work on that site, but I do not believe you are using them.
Let me know if you’d rather reconfigure that site to use www as the primary custom domain (click “…” next to www.beam-commerce.com here: Netlify App and then choose “set as primary custom domain”) or if you’d rather keep www/bare domain served there with bare domain as primary, and you instead deploy a second copy of the site using some subdomain (I recommend netlify-placeholder.beam-commerce.com or something equally intuitive) and I should apply the setting there.
No, it is not going to be possible on a single site. you can of course set up a second site to serve the other names like store.site3.com using the same settings as the first, and make sure to deploy both when you have a change to the website code.
I don’t think that would work. You’ll need to actually have the same content deployed to that second site instead of using a redirect rule like you mentioned.