I ran into issues with conda and OTB and then I saw https://gitlab.orfeo-toolbox.org/orfeotoolbox/otb/-/issues/2053
There are also other issues reported.
I did a quick and dirty packaging of OTB 7.2.0 with conda. It uses python 3.7 and if you need gdal, you must use gda=2.4.1
There’s a binder demo at: https://github.com/fabricebrito/conda-otb