This question will be resolved on the basis of the 2023 General Social Survey (GSS). This will be released sometime in 2024 (the specific date is yet to be announced) but will cover data collected in 2023.
Specifically, I will use the 2023 percentage listed on this page to resolve the question. If it is 50% or above, this question will resolve YES. If it is below 50%, it will resolve NO. If no report is released, for whatever reason, the question wil resolve N/A.
The full question text is "I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in them?" The Supreme Court is one of multiple institutions asked about, with the others also listed on the GSS website.
You can read about the methodology of the 2022 GSS further here.
For context, 35% of those surveyed in 2022 responded 'hardly any confidence.' This was an increase of 14 percentage points from 2021, when the figure was 21%. The figure in 2018 (the third most recent survey) was 14%.