I don't know how other countries deal with treaties, but the USA tends to ignore all the treaties it has signed unless it has also created a statute in federal or state law to enforce it.
The US is actually quite far in the "monist" side of the spectrum when it comes to ratified treaties but it has such a divided and dysfunctional political culture coupled with an executive which has wide latitude in foreign affairs that many agreements are signed up to by the executive without being ratified by the senate. Monism basically means that properly entered into, international treaties have force as domestic law as well.
The UK is one of the world's most dualist countries. No treaty has any domestic legal standing whatsoever. Until 2010, the government of the day could ratify treaties without recourse to parliament although there has been an observed rule since the early 20th century called the Ponsonby rule that parliament have time to debate and vote on important treaties. The government cannot make domestic statute law without a parliamentary vote therefore dualism emerged.
This means that the UK has to pass a "back to back" law to give legal effect to any treaty it signs where that is required. The US only has to do so when there are elements of the treaty that are plainly not "self executing" i.e. if the US signs a treaty creating a personal right for its own citizens then no further legislation is required but if it signs a treaty agreeing to do something that requires new appropriations, a new agency, or whatever then additional legislation is required.
Quite a long-winded way of saying that Assange never had recourse to certain claims his legal team attempted to make about conflicts between his treatment and the extradition treaty - the extradition treaty does not directly drive UK domestic law on extradition.
