Framework

Find a reputable, professional board-level electronics repair specialist in your area. Probably won't be free but they should have plenty of experience to help you safely fix up the pins. Afterward you should assume it will break if you do anything to mess with the connector going forward - Pins can only be messed with so much before they snap. Depending on the pins - I haven't seen them in person - An electronics repair specialist might still be able to replace an entirely broken/missing pin though its not a situation you want to be finding yourself in to begin with.

Bending pins back into place isn't automatically a major challenge. There's actually a very easy way to do it if the pins aren't too overly fragile. But given the connector you have trouble with is critical to system function and the cost of a full board replacement quite expensive... Its not a fix I'd recommend doing without experience (I do have some experience fixing pins and I still wouldn't touch a battery connector).

Because you're dealing with power do be careful messing around with the connectors. You could easily damage the connectors, pins, or board as a whole beyond economic repair. Also lithium batteries are prone to exploding and catching fire if they aren't properly handled/wired.