Many times I just need to export some data or do something without starting ArcGIS Pro and opening a new or existing or a blank template. Just open Catalog, do what I have to do and exit.
Have you seen this idea: https://community.esri.com/t5/arcgis-pro-ideas/offer-a-standalone-arccatalog-replacement-for/idc-p/1693588 ?
Also this will probably not satisfy you, but there is a blog post that goes through how to mimic the old catalog experience as closely as possible.
Dude, where's my Catalog?
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