And Biden has gone on record as saying his goal was to get more conservative judges into the court to overturn Roe v Wade
So do you have an actual source for that? I checked, and found nothing, particularly nothing in that direction that's too young to legally drink. His history on the subject is pretty sub-par, but most of the worst of it seems to be as old or older than me.
His current actual stated position is to set roe v wade as straight up federal law, though, near as I can tell. Seems fairly firmly on the "personally uncomfortable, publicly supportive of legal protection" side of things.
It's extremely mixed. Yeah, his publicly stated position is that Roe v Wade is "the law of the land". Though what I see isn't that he pro-actively states the intention to codify it into law. He says that he would work on codifying it into law if its status as a legal precedent were endangered somehow.
On the other hand, he still supports the Hyde Amendment even now. Which basically means that he's on the slimy side of won't tell anyone they can't, but will make it difficult/impossible for whoever he can, with coincidentally classist/racist consequences. On top of that, his reason for supporting the Hyde Amendment is stated to be "Those of us who disagree with abortion on religious grounds shouldn't be forced to pay for it." He considers his position and voting record to be a compromise between respecting people's religious beliefs against abortion, while not forcing their religion on others. Except it is... just tangentially instead of directly. It's straight up 20-years-ago republican style religion-based legislating.
And of course, as I've said plenty of times before, platform doesn't matter. Record and funding matters. My assessment is Biden would put moderate effort into preventing abortion from becoming explicitly illegal, but that is as far as his support for abortion rights would go. And if any new schemes were invented during his term to make access to abortion more difficult without explicitly illegalizing it that he would support them.