I have an inner monologue when reading (or otherwise interacting with language), but mostly not when actually doing stuff. There must be some stuff you do where you don't have an inner monologue? I think it's a matter of degrees, like when programming my inner monologue consists mostly of variable names, but not like a procedural "I'll do this, then this, then it will do this".

If you're having a hard time grasping that, try doing or thinking about things while doing a mantra. I think you'll find that you're still able to "think" while the only thing your inner dialogue is saying is some kind of mantra. (It may take some practice)

You can also try speed reading apps which force you to absorb information without the time for an inner monologue.

I find this helps with introspection as you can observe ideas without the (direct) bias of language. Being able to recognize and observe the thing that's making your inner monologue happen is a useful skill, I think. I can't really imagine being bound to language like you're describing, and it often takes me a while to put more complicated ideas into words.

Languages categories are never going to be accurate. Is a whale a fish or a mammal? Well technically a mammal, but if you want to put someone in charge of them it's probably better if it's the department of fisheries than whoever's in charge of buffalo. One of of them has boats. The word is just a word, a pointer at a vague collection of things with similar properties. Being able to think about and work with the things directly without the distraction of language is very important to me.