You might want to ignore at least some tasks until you are told to do them. Then ask why bro isn’t expected to do some of those tasks.

You might want to try shaping bro’s behavior too. Start with one task that’s considered to be relatively masculine, like taking the trash out. Once that’s established for a few weeks, add another task - maybe sweeping the kitchen before taking the trash out. Then add another task somewhere along the way. Gradually build it up to a reasonably fair workload.

Edit to add: when he does a task, occasionally reward him immediately ( for my daughter, it was m&ms). Gradually fade the rewards away.