How to find all WGS assemblies accessions of a species

Some background

Similar to the OP of https://www.biostars.org/p/377840/, I would like to programmatically BLAST a sequence to a local database of all WGS assemblies.
Since this isn’t feasible for the average biology lab server (correct me if I am wrong), I plan to use ncbi-acc-download to download all WGS assemblies of the species of interest (not a popular species like E. coli, so it should be feasible). Then, I will create a BLAST database for the downloaded assemblies and BLAST the sequence to it.

My question

How can I find all WGS assemblies accessions of a species?

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My current plan is to search the NCBI Assembly database using Entrez and a search term such as "wgs"[Properties] AND txid1337[orgn:exp].
EDIT: IIUC, this approach might miss some WGS assemblies. See my answer.

I am worried (and thus ask for your help) this isn’t the right approach because there seem to be at least 3 other places in which assemblies can be found:

• The assembly_summary.txt files that are described in https://ftp.ncbi.nlm.nih.gov/genomes/README_assembly_summary.txt.
• https://www.ncbi.nlm.nih.gov/Traces/wgs/. This is the one I am most worried about. Both because it seems to have much more entries, and also because https://www.ncbi.nlm.nih.gov/genbank/wgs/ says: "The public WGS projects are at the list of WGS projects ."
• taxid2wgs.pl. (As mentioned in https://www.biostars.org/p/377840/#471535, this one seems to miss some assemblies.)