If you just acquired a domain name (with or without email accounts), this wouldn’t work out of the box.
First, you’d have to find a way to make your domain name point to your IP address, which is the IP your ISP assigns to your router, and thus likely to change every other day, so you’d have to enlist the service of a dynamic DNS provider that takes care of this as well.
Then you’d have to decide whether you’d establish routes and port forwards to devices behind your router (like Pi-hole) to make them publicly available via your domain name, which in turn implies to setup your firewall correctly etc. etc.
For most home users, this is clearly not something they strive for.
And if you do that the wrong way, you might end up routing your DNS traffic through public internet, which is both slower and more insecure than keeping it local (though I am insinuating a major misconfiguration here).
If you just want to use your domain name on your local network for vanity reasons, you could add a respective
.com entry to
But even then, you should be careful as to not blocking yourself from access to your mail, which -as I presume- is hosted by the vendor who provides your domain and uses the same domain name.
Thus, my strong advice would be to stick with
.local (unless you are not only familiar but at ease with points I’ve raised).