I strongly recommend switching to SRA https://www.ncbi.nlm.nih.gov/sra
Whether the following would work ...
esearch -db sra -query "{species name }" | esummary
I'm not at all sure because SRA has its own toolkit. Maybe NCBI e-utilities e-summary efetch would work on the SRA database. However, the weblink certainly works for transcriptomics.
NCBI has shifted some of its database to be housed off-site onto GCP and AWS and I have a feeling these may not be accessible to e-utilities, but I could be wrong.
Just to note, what I envisage the question meaning is a complete transcriptomic study for a given species (or given sample) under given experimental conditions.
Comments. I better clarify, SRA will be raw Illumina output, it is not assembled into exome cDNA. e-utils is basically for assembled cDNA, it might give you the information - I really don't think it will download it though. So to answer your questions, yes the data will be there on SRA, whether this is the format you want is a different question.