I have also had this issue where the multidimensional tools are not reading s5p L2 files - https://desktop.arcgis.com/en/arcmap/latest/tools/multidimension-toolbox/an-overview-of-the-multidimension-toolbox.htm
e.g. make netcdf feature layer is unable to read the variables. (https://desktop.arcgis.com/en/arcmap/latest/tools/multidimension-toolbox/make-netcdf-feature-layer.htm) whereas if the files are read in as you have said they will read in the variables correctly.
I have contacted ESRIs email support regarding this issue (a few days ago) and they have someone investigating it but I do not think they will come back with a solution. If they do offer a solution i will post it on here.
ArcPRO 2.6 is being released in a week or so - they have apparently made several updates for working with netCDF and multidimensional files - perhaps within this update they may have solved the issue of reading in S5P data.
I am currently looking to use the HARP library to convert L2 CH4 files to L3 gridded files and then read the files into a GIS afterwards.If anyone else has any advice for working with S5P data within ArcGIS (or QGIS) then I would love to hear from you.