Laundry room has mildew smell
We have had an HE washer since 2003, in 3 different homes, and it has done what you describe in all of them. As far as I can tell, it has to do with a couple of issues. A) the detergent drawer and the liner around the wash drum hold water after a wash B) the waste water lines seem to not drain off completely between washes.
Our solution has been to leave the door to the washer and the detergent tray open when not in use. This allows them to air out and not gather the musty smell. I also took my machine apart last summer and cleaned ALL of the water hoses, which had an accumulation of mildew in them (I would just replace them next time, as it was a PITA to get them clean.)
That's just my opinion. But it's free, so take it for what it's worth to you.