The charges the US attempted to extradite him for were based primarily on things he did or allegedly did or which came to light after the rape charges.
Ockham's razor also applies. If you want Assange charged in the US on 'espionage' or similar and you have a choice of notifying the Swedish authorities that he is wanted for serious crimes in the US or instead relying upon separate local allegations that are so vague the Swedish legal system has to work its way through an appeals process to even decide to whether to pursue the case or not whilst leaving him at liberty to leave the country, you're unlikely to choose the latter.
> A state wishing to prosecute a surrendered person for offences committed before his or her surrender, or extradite a surrendered person to a third state, must, subject to certain exception, obtain the permission of the executing judicial authority. Such a request is made in the same form as a European Arrest Warrant, and granted or refused using the same rules which determine whether surrender would be granted or refused.
> the fact that the US has now tried to extradite him proves that.
It proves they care now, under a wildly different (and totally clownshoes) DOJ, which if anything lends more credence to the theory they did not care back then or we would have seen them try back then.
Which means very little - the fact that the US has now tried to extradite him proves that.
> extradition from Sweden would still have required extradition from the UK since he would've been serving time in both countries.
How so? AIUI Sweden would have notionally promised not to extradite him, but there was little mechanism to enforce this.