None of the above have have primacy over national law of independent nations unlike the EU, and its only the European Union that has the ECJ which has fairly broad powers in many aspects of national and local laws even down to the mundane of perhaps needing accident insurance whilst riding a lawn mover on private property.
As for NATO you really want to compare a defence treaty to supranational institutional instrument which uses its power to form laws, treaties etc with non member’s, good grief
Actually, why wouldn't you?
Look, there's no doubt the European Union is by far the most important and influential supranational organisation in the field of economic collaboration, despite not being the only such kind of an organistation out there and the reason for that is to be found in it's uniquely deep integration, which makes outsiders consider at it as one -rather than 27 diffferent- counter party, similar to how NATO is (designed to be) perceived as a monotithic defence bloc too by treaty: notably article 5 effectively does that, but it also means members have given up on some very important element of their national sovereignty too: i.e. that of opting to stay neutral in a military conflict in which they are no party!
I'd say the commitment to ultimately go to war over something which is in essence none of our business is a bit more far reaching than the obligation to take accident insurance for a lawn mower, even though I agree that in our day-to-day lives we luckily come accros the later more often, than we ever will with the former, but still... the transfer of this ultimate element of a nation's independent sovereignty has happened and is still very much out there, ready to be used.
To translate it to today: if Putin were to be willing to put his hand on a part of the Baltic states for instance, BoJo could not do what Chamberlain did in Munich and fly to Moscow to sign them away 'to respect the desire of the British people never to go to war again'. He'd be in Brussels the same day to put his signature under a very strong NATO statement laying down an ultimatum to Putin: I'd say that's a MASSIVE transfer in sovereign decision making of any government of a NATO country to the supranational structure of NATO as forseen by its treaty, don't you agree?
Shouldn't you be pulling out of NATO too then (there's an article to do so under the NATO treaty, and it reads remarkably similar to article 50 of the TEU, btw), to regain full military sovereignty, so you can take back control over military operations currently conducted on your behalf too, can stop the spending on unelected bureaucrats sitting in HQs near Brussels and to happily diverge on all common military production, training and operating standards now solely set by NATO so the UK's military and its industry could finally work together with emerging military powers like for instance the PRC too and become 'Global Britain'????
According to some in the Pentagon, this would be in line with Trump's thinking too (on some days at least...), so copy-pasting this 'strategy' would definitely help the UK in being fasttracked to become the 51st US State, an ambition that seems to be gaining mommentum in the minds of some, not at least the US born British PM.