Not keen on hcaptcha because I'm almost always need to solve 2 sets of the puzzle vs 1 with recaptcha. Theres a thin line between privacy and convenience, most of the time I've felt hcaptcha to be on the least convenience side.
Even when some service allow registering using good 'ol email, some still refuses to accept any non gmail/outlook address. Met a service that wouldn't allow me to register using my own domain email address a week ago. Baffled me staring at the google, fb and twitter sso button with the form for email address giving error of "please use an email address from a reputable provider".
If you're not going to build a website on the domain thus won't be bothered with seo and stuff, why .com? There's countless other tld thats cheaper than .com's $8 yearly (which imho still cheap considering some tld do goes to $50-100 yearly). Check https://www.domcomp.com and see the new and renew tab then choose the overall cheapest there.
For email hosting, again for the absolute cheap theres actually few free service that allow custom domain, zoho and yandex comes to my mind.
Not op, but what you described is called a catchall address. Easily done with custom domain. Basically a regex for *@domain.tld, every mail sent to (anything)@domain.tld will arrive at a preconfigured mailbox, say admin@domain.tld etc