A FAQ here answers your exact question (which you have also quoted). For gnomAD v3.1, this section of the downloads page will give you VCF files containing genotypes called at that variant site and a separate metadata file as well. Do make sure you read through their linked blog post, it's mentioned that they aren't making all the data publicly available.

If you want a better resolution, then their publication has something to say. Page 59 of their supplementary information states that they have used GTEx v7 gene and isoform expression data. This has been accessed from NCBI dbGaP accession phs000424.v7.p2.c999. This data seemed to have moved to v8 available from here. Its access is restricted, you'll have to make an authorization request to use that data.