An update: The backhoe knocked down most of the wall, and I'm slowly but steadily getting the blocks resituated on pallets to sell for most of what I paid for them. The learning experience was inherently valuable.
The plan: rebuild the wall with an appropriately dug footer, using natural native stone approximately 4'x5'x1.5', with Type S mortar and smaller native stone pieces between them. This way the wall and waterfall will blend fully together, as it was previously, except with mortar and larger rocks so the wall doesn't blow out this time.
Native stone looks so much nicer than landscaping blocks. 4'x5'x1.5' stones? I am imagining something like
this? But these are more like 4'x2'x1.5', so I am a little confused. 4'x5'x1.5' stones would be massive. Stones that size will give you wonderful support and you won't need any mortar or rebar after stacking those massive babies on top of one-another. Also, mortared or concrete walls require footings dug below the frost line else they risk buckling due to frost heaving (unless you live in an area that never freezes, you didn't fill in your profile so I don't know where you live). An unmortared wall is a little more forgiving in that is can flex a little where a mortared one just cracks, although with those size stones I doubt frost heaving will ever be a problem.
You never want to mortar a retaining wall that is holding back soil (or anything that needs to drain). If it's a pond wall and you're waterproofing the inside of it, that's another ballgame because you're addressing the water in another manner (with a liner), but you don't need mortar if you have these nice big stones. Or are you saying you have smaller rock and you plan to build the wall to be 1.5' wide and 4 or 5 feet tall? A 1.5' wide mortared rockwall of 4' height is probably going to need a lot of rebar.
https://www.artofstonegardening.com/limestone-iron-wall shows what looks to be about a 1.5' wide and 4' high stone wall with rebar that isn't holding back anything: they say the rebar is necessary due to the thinness of this wall, and this wall is just a wall that is not retaining anything. I personally would never build this type of stonewall. I only build
dry stonewalls. Maybe someone here has built something like you are and can be of more help. Please post a photo of your new stones when they arrive so we can see your new materials. I'm sure they will be much better than those landscaping blocks!