That isn't how the ECtHR works. Cases are brought by individuals, or very occasionally by other states, against states, on the basis that X events happened, Y legal process took place, and Z verdict which the appellant doesn't like was returned from the top level of the process. Check out Article 35 of the convention here. https://www.coe.int/en/web/compass/the-european-convention-on-human-rights-and-its-protocols
So what would have to happen would be that a trans person would have to want to do something (e.g., use a changing room reserved for the opposite sex), and then they would be turned down (or arrested for going in anyway), and then they would sue the leisure centre (or be taken to court and charged with whatever the actual legal offence is), and it would then go through the UK courts, and end up at the Supreme Court which would say "the leisure centre was within its rights to not allow access to the women's changing rooms to someone who is not a biological woman, per our April 2025 judgment", and then the trans person would submit their case to Strasbourg.
The case last week on which the Supreme Court ruled can't go on to the ECtHR because it was a win for a group of citizens (For Women Scotland) and a loss for the NHS board (although the actual respondents were the Scottish government ministers). A government organisation can't appeal to the ECtHR more or less by definition, because nobody in the management of the East Fife Health Board or the Scottish government has had their human rights reduced by this decision. Jolyon Maugham can announce that he's going it for the shiggles, but it won't get anywhere.
(In fact, had the SC verdict gone the other way it probably wouldn't have been appealable to the ECtHR either, because FWS brought the case in the civil courts against the ministers. Sandy Peggie, the person whose rights were directly affected, wasn't on the docket as far as I know. However, I think I'm right in saying that her employment tribunal case is still going. In the event that she were now to lose that, she could then go through the rest of the legal process and ultimately it might end up at the ECtHR. But in view of the SC ruling this seems vanishingly unlikely, and I assume the health board/Scottish NHS/government will now fold.)
It may also be worth remembering that the SC decision is strictly only about people with a Gender Recognition Certificate. Even if the decision had been appealable to Strasbourg, any verdict in favour of the trans side could only have been valid for people with a GRC, which the majority of trans-activist people don't have because TRAs are all about self-id.