... There is no 'Supreme Court' for nations: there is (at the moment) only the Security Council of the UN. Everything else, including all the wibbling shite that passes for the UN General Assembly, can be safely ignored. The rest is politics (including the application of WTO tariffs, etc.).
A point made on 1 Oct 2020 and over 1,000 pp ago (according to my phone pagination) in this very thread, when discussing the EU’s threat to take legal action against the UK over the, then putative, IMB.
The only available legal forum is the ICJ, and enforcement of any decision is devolved to the Security Council.
The EU, qua EU, is not, and can not be, a member of the Council because it only has ‘enhanced observer’ status and a legal personality equivalent to thee and me. In that respect, the EU can not bring a case in the ICJ, only a sovereign state and full UN member can do so.
In any case, even if the EU does somehow finesse a case (very doubtful), and the Court found against the UK, enforcement is down to the Security Council where the EU is not a member and the UK has a veto.
As you say, a toothless threat, and the UK Govt knows it.