It sounds like you have something less than full aphantasia. Remember it's a spectrum, not a binary.

For me with your triangle example, I know what the equilateral triangle and the parallelogram look like. I could describe them, or draw them, but the whole concept of a mind's eye is completely foreign to me. I don't have any ability to put something in my mind's eye and I guess I conceptually understand what people probably mean by "mind's eye" but I have no experience of it. I conceptually understand things, but there is no imagining happening for me.

A better example might be the brain teasers where you have a cube laid out in 2 dimensions, and you need to fold up that 2 dimensional cube and 'create' a 3d cube and manipulate that 3d cube to solve the brain teaser. From what I understand, most people can do this either completely in their head, or else in their head with some drawing.

The only way I can solve these is to draw the cube with pencil and paper and then use logic while looking at the drawing to figure out the answer. I just have zero ability to in any way create or manipulate a 3d cube in my head. If you took away my pencil and paper I would resort to trying to put together a chain of logic ... "if this side is X, then that side must be Y and the reverse side would be Z" but that quickly becomes confusing and hard to manage.

I also don't experience anything visual when I dream. This is actually how I found out I have aphantasia. I was trying lucid dreaming and none of the instructions made any sense. How am I supposed to fly when I don't have a body in the dream? How am I supposed to flip light switches when there are no light switches?

The cube test is an interesting one, but, to pile on another stupid internet trend, that seems more like a "shape-rotator" vs. "word-cel" question. For very simple fold-ups I can do this, but for more complex decompositions (like if you have me an octahedron) I doubt that I could reliably do this.

In terms of the triangle attaching, is it that without drawing you would not be able even to say what the resulting shape is? If I threw in a third triangle you wouldn't be able to tell me what the shape is now? I'm trying to see if I can get a clear discriminator that tells me whether I am different from you in how I am able to visualize or if we're just using different words (or if I, too, am aphantashic and that other people have powers beyond my ken).