The court has published further details of the appeals - R (on the application of AAA and others) (Respondents/Cross Appellants) v Secretary of State for the Home Department (Appellant/Cross Respondent) - The Supreme Court
and this was itself an appeal from the High Court - AAA v Secretary of State for the Home Department (Rwanda)  EWHC 3230 (Admin) (19 December 2022) (bailii.org)
The Court of Appeal judgment is discussed on this blog at Law and Lawyers: A note on AAA v Secretary of State for the Home Department ~ removals to Rwanda (obiterj.blogspot.com)
The current Home Secretary (Suella Braverman KC MP) doubtless has a lot of political capital riding on the outcome.
A government "win" will probablyencourage the government to put into practice its agreement with Rwanda at the earliest possible moment. If the government "loses" then there will doubtless be further cries from some politicians for the UK to denounce the European Convention on Human Rights.
In truth, whatever the outcome, the judgment will be unlikely to give the government a blank cheque to just simply remove individuals to Rwanda. In every single case it is likely that the decision will require that a deportation is lawful in the particular case and, if it is, the government will have to ensure that procedural safeguards are applied scrupulously.
We shall see ..... I leave comment about Braverman's political position to those who write and comment about politics !
Here is a list of the appeals as published by the court .....
Update 16 November 2023:
Braverman left the government on 13 November and was replaced as Home Secretary by James Cleverly MP.