This is a thorny question I’ve discussed with a lot of native French speakers, only to find that even my French colleagues seem to be split over this grammatical point.
I instinctively choose the following constructions in conversation, and for some reason I can’t quite put my finger on, I notice I don’t opt for the reflexive construction for the 2nd sentence with “rien”.
Some native speakers don’t agree with some of them, while others give them the green light. The 4th one with “mieux” is an especially controversial construction.
Tu t’y connais en menuiserie, hein ? { reflexive }
Je n’y connais rien en menuiserie. { non-reflexive }
Je ne m'y connais pas beaucoup en menuiserie. { reflexive }
Personne ne s’y connaît mieux en menuiserie que Felix. { reflexive }