Phone switches off unless cover is removed: Redmi Note 4x, new battery

I just replaced the battery of my Xiaomi Redmi Note 4X (mtk version) with a new one (both the old and the new one have the code BN41, not BN43).

Without the back cover, it works perfectly. However, when I re-mount the cover, it’s impossible to switch the phone on. I tried plugging it to a charger or to a PC, but it’s useless: it looks like it’s bricked.

If I remove the back cover I can switch it on again, and it works seamlessly. I tried doing energy-intensive operations, and the battery lasts long, so I am inclined to think that it is not damaged.

However, if I put the cover back on while the phone is turned on, it switches off after a (somewhat unpredictable) while, and there’s no way to switch it on without removing the cover again.

The flexible buttons seem to work well. I checked the battery connector (and the other main connectors) multiple times, so I feel pretty confident those are ok.

Any ideas on how to solve it?