This odd URL redirect seems to have happened August 12. In Trump's Wednesday press briefing, reporter Chanel Rion from One America News brought it up, saying that the redirect had evidently been put in place within a couple of hours before the press briefing. And, yep, it's still there.
The IP resolution for the hosting server is 192.64.119.246, which is in one of Namecheap's allocations, 192.64.112.0 to 192.64.119.255. So all that someone is doing is likely nothing but entering Biden's website in a field at Namecheap and clicking "Submit" to accomplish a basic 301 redirect. You can do the same thing with any GoDaddy account; no separate hosting server or any technical knowledge required.
There have been a bunch of changes related to this domain name since it was first registered in 2002. A stupidly expensive (I had a friend with a company account look it up for me) source for that is "Whoisology.com"...it's kinda the "Internet Wayback Machine" for domain names. The first archived entry they have is from December 2012. From that date through the September 2019 entry, the domain registrar was DomReg (
https://www.domreg.lt/) a registrar service in Lithuania. It was registered anonymously there, as well; but I'd say there's a decent chance the registrant was east of Poland: if I were to bet a dollar, I'd wager it on Belarus, Ukraine, or Russia.
Sometime between September 2019 and December 2019 the domain name either changed hands or expired and was salvaged by someone else. As of that date it was resident with its current owner and registrant at Namecheap in Los Angeles.
Still doesn't tell us squat about who and why, but reveals a tiny bit more about how and when.