Thanks to ss888us for providing the info. We've tracked this down - there are actually 2 issues but neither are related to the WordPress duplication, that part is coincidental.
The site had a "drop-in" plugin which our plugin manager doesn't recognise. This is fixed in 8.2.0 and this will fix the plugin listing.
There is also a user with a role which the plugin manager can't handle. We need to do more testing on this one.