It's really hard to say without being there in person. The wall certainly looks unstable and ready to be taken down, but a lot of concrete walls can look terrible, but still be structurally sound. We owned a house with a concrete block wall reinforced with rebar that had perhaps a 10 degree lean outwards that looked like it'd fall any day, but it took a LOT of sledge hammering, chiseling, jacking, and gas-powered diamond-blade cutting to actually get it out. It likely would have stood for another 50 years on its own.
In your situation, it appears that you've lost all the earth around your footing. At this point, it may be a lost cause and you'd be best taking it out. Ideally, you'd then replace it with a stepped retaining wall using a dry-stacked block. The dry-stacked blocks are a) easier to install and b) when installed properly will allow water to drain through rather than build up behind the wall pushing it out.
All that said, it appears that your neighbor has build a foundation right up along your wall. I don't know where you live, but I'd think in a lot of places that'd be against code (you typically can't build that close to the property line). In addition, it seems risky for them to depend on you to hold up their foundation with your wall. Seems that they should be bearing part of the ownership of whatever is retaining the earth on this property line.
Finally, if that's a down-spout in the lower photo emptying between the two walls, then a) take it up with the city, as that is likely also breaking all sorts of code regulations and b) your neighbor really should be worried about that. You don't want a downspout draining near the footer of your new kitchen's foundation.
Load bearing or not, a concrete block wall needs a footing beyond what your questionably thick slab is.
That is why it might fall down, aside from not using tie-ins. AFAIK, you shouldn't have to tie-in at the ceiling, just to the side walls. I'd hope any professional would be talking about (a) pouring a footing (b) drilling holes everywhere for rebar and (c) making pockets for tie-ins. But it's a bathroom; not a vault. No one does this if they can just frame out the wall with lumber.
Ad hoc masonry must be tied-in to the existing structure:
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Blocks are very strong under compression from above, so if the walls are bowing under the weight of each course of blocks, that makes me think the walls are not plumb. You would need to tear down the walls and redo them to be plumb.
You say you want your walls to "withstand the pressure of the dirt." Are you burying the structure? Correctly-built block walls may be strong under compression, but they are weaker under pressure from the side. Tread very carefully. It sounds like you may want to involve the services of a masonry professional if you're not sure how to build a block wall in such a manner as to prevent it from collapsing under whatever loads you're putting it under. Built correctly, block walls are very strong. These blocks are resting on a concrete foundation, right? Ideally you would have a concrete foundation with rebar sticking out of it that you would place the blocks over such that the rebar goes through their cores, and then you would grout or concrete the cores to tie the blocks into the foundation. Block walls are very heavy. Without an adequate foundation, the structure is doomed from the start.
If your block walls are not straight, plumb, and tied into an adequate foundation, you'll need to redo them so that they are--end of story. If all of that is fine, there are a couple of ways you can reinforce your block walls to increase their resistance to exterior pressure from a bunch of dirt:
Do both, and the wall will probably outlast your great-grandchildren.
But again, I would strongly recommend hiring a professional to help you. You don't want to build a structure that's unsafe. Masonry is heavy. If it collapses when someone's inside it, that person is probably a goner.