HAProxy, nginx and even Apache2 itself can somewhat easily rewrite the FQDN in an incoming URL. But you'll need a bunch of machines to do it. The definition of "bunch" depends on how much traffic you have and where it's coming from.
So... very much possible, but it will cost some money.
In fact, even their official brand kit is still... Twitter's brand kit. Unchanged: https://about.twitter.com/en/who-we-are/brand-toolkit
This is what happens when you rebrand with zero planning and without telling your own employees about it ahead of time.
Fixing all those "remnants" of the Twitter brand will take the work of hundreds of people countless days, and yes there's a risk of breakage, as with any change. Work and risks which are completely pointless, as it's a needless brand change.
It's still up in the air whether they'll start making real changes, like twitter.com redirecting to x.com instead of the other way around.
Why?
Because aside from being unprepared for it, a tons of problems are cropping up with the X brand, such as people's negative reaction to it, and the legal issues of thousands of companies in the US and around the world having registered the X trademark for various applications, including payment apps, video apps, chat apps, messaging apps.
This means if Musk proceeds, he may get a bunch of trademark violation lawsuits on top of all other lawsuits he's dealing with.
I expect in a week or two, he'll play it as "lol just kidding, it was a prank bro" and revert to the usual Twitter brand. He always does this when he screws up, and unfortunately I'm painfully aware of the pattern at this point.
Unfortunately he already defaced the Twitter signage on the SF office. But at this point we can only shrug and accept Twitter is going down the drain anyway, so who cares.