For HLS NASA requirement was capability of delivering 2T of cargo to the Moon.
Starship offers 100T or more.
Edit: I was referring to the Starship HLS variant linked to
Starship is first and foremost designed to deliver people and/or 100T of cargo to Mars.
It most likely never will be according to criteria from commercial crew program, because it does not have and will not have an escape system.
That said, they could update the page, it's 2022 already and promising great things in the future year of 2020 is not a good look.
And while I do not want to besmirch SpaceX engineers working on it, the website is not a statement from them, it's a statement from PR machinery. Which holds similar weight as "FSD is next year" being told for 7 years by Tesla PR.
If they manage it, congrats. If not, I still reserve the right to laugh at the PR machine (not at the engineers, they have a hard problem to solve that isn't helped by overpromising PR).
I do not have high hopes in that design.
Starship doesn't exist.
The SLS block 1 can put 95 tons into low Earth orbit. Compare to the Falcon Heavy, which can put 63.8 tons into LEO. Is it worth paying over ten times as much for only 1.4 times as much cargo?
That said, majority of the price tag is probably congressional impact rather than anything else...
Now we will soon be able to do it again.