The battery arrived from Amazon, but it’s not the one depicted. 😕 It’s too thick, too long, too narrow, and the connector is wrong as well. Even the wires off the battery are too large. I’m returning it.
I guess I’ll get it from Aliexpress. That one has both 1000mAh and 1300mAh capacity. Maybe they couldn’t make up their minds.

At least judging by the photo, it looks like it’ll fit, the wires seem the proper gauge, but I’m not sure about the connector. The photo doesn’t show any details.