The Taliban bought two names for their English-language website: alemarahenglish.com and alemarahenglish.net and these were up for at least two years that I know of.
Then the US went to the site that sold them those names and had both names removed from the nameservers, so attempts to connect just say, 'Hmm. We’re having trouble finding that site.'
So the Taliban bought a .asia name, and their website was up and running. But not for long. As soon as the US found out about the .asia website, they went to whomever sells .asia names and had the Taliban names removed from the nameserver, so if one tries to connect to their new, .asia site, one gets "Hmm. We’re having trouble finding that site."
There are several neighbours of Afghanistan who could help, but it is not clear if the Taliban can work with any of them. They figure Iran are all infidel apostates who must be killed for their apostasy. The CIA agency National Endowment for Democracy has lied to the Taliban (and everyone else) that the PRC is committing genocide on the Muslims in Xinjiang, so the PRC is out. And the Taliban were created by the US for the specific purpose of killing all Soviets in Afghanistan, so they are officially designated as terrorists by Russia.
The Russian Embassy in Kabul is fully open and fully staffed, but Russia have not recognised the Taliban government. The PRC Embassy in Kabul is still open, but was reduced to a skeletal staff, and the PRC have not recognised the Taliban government. And I haven't heard the status of the Iranian Embassy in Kabul, but I know Iran has not recognised the Taliban government of Afghanistan.
So the three nations that could help the Taliban get their website back up, nations that border Afghanistan, don't seem to be readily available.
(They should probably try Pakistan.)