Getting Unique Identifier List for GEO Datasets NCBI
You can use Entrez Direct for this. The following returns Unique Identifiers which are just bare integers.
$ geo_query='&quot;Expression profiling by high throughput sequencing&quot;[DataSet Type] AND (&quot;Homo sapiens&quot;[Organism] OR &quot;Mus musculus&quot;[Organism] OR &quot;rattus norvegicus&quot;[Organism]) AND (&quot;2020/01/01&quot;[PDAT] : &quot;3000&quot;[PDAT])'
$ esearch -db gds -query &quot;$geo_query&quot; | efetch -format uid &gt; gds_results.txt 
$ wc -l gds_results.txt 
9981 gds_results.txt
$ head -n2 gds_results.txt 
200134092
200120931

Instead, if you are looking for a way to get the GSE accessions, you can use the built-in xtract command to parse the XML returned by esummary as follows:
$ esearch -db gds -query &quot;$geo_query&quot; | esummary | xtract -pattern DocumentSummary -first Accession &gt; gse_accs.txt &gt; gse_accs.txt
$ wc -l gse_accs.txt 
9981 gse_accs.txt
$ head -n2 gse_accs.txt 
GSE165829
GSE165824