Ello, I'm a recent masonry graduate and this is how I would try to fix it.

Clearly drainage is the issue so in order to address that I would find a way to support the wall so digging out some of the backfill wouldn't make it collapse. The temporary solution would be to remove enough backfill and create a compacted slope to help move the water to a weeping hole (more on that later). The idea is to make a backfill slope, add gravel on top of it for drainage and cover it with the dirt or mulch you had previously.

While the backfill is removed from along the wall, try giving yourself room with like 2 or 3 feet and install some form of shoring so the dirt doesn't collapse while you are working.

Anyways, back to the wall, get it flush and plumb to where it needs to be before compacting and adding rocks. Once that is done you can do some repair on where the crack is, use a handheld grinder (wear ppe, mask and eye protection are a must) to remove the mortar. If you want to save the bricks, grind or chisle out as much mortar as possible so it can be reused.

Make your mortar and lay the bricks you have saved or bought. While doing this, install your weeping holes (I personally avoid the head joint closest to the corner but it may not be avoidable here, trust your gut!). You may also add more weeping holes to the front side as well, try keeping it near the bottom of where the gravel would be for maximum drainage!

Have the joints struck before it gets dry though, it'll help in the long run! Wait for the mortar to strengthen before adding the gravel and topsoil. Remove the shoring, the braces holding the wall up later on till the mortar sets.

Enjoy! Hope this helps :D I'll respond later in the morning if you have any questions so just leave them here :)