Yes, all tracks of math involve people using math. Proof writing is a part of use for a lot of it. There are also very many tools within the use of proof writing where a lot of education is around learning a bunch of tools so that you can better "recognize which tool to apply, then apply tool", in a future real-world use where you want or need to prove something.

I'm a little snarky, but you have a broken idea of what math is. It's not even your fault. I don't even claim an unbroken idea for myself, I went through public education too, though I do think it's less broken. Somehow compulsory education has managed to get near universal basic literacy, but seems to have failed on whatever equivalent some sibling comments have hinted at exists for math or at least mathematical reasoning. A lot of algebra work taught for junior high can be understood as just a foundation to be able to understand later things (though you can of course use some of it directly as taught without having to learn more for every-day things like some boy scouting activities, or helping with putting together a garden or a fence, or programming -- and some of course is entirely useless). But instead of pushing algebra even earlier, states are instead moving to push it even later. (Let alone trying to spread awareness of even a hint of the subtle divide between more general algebra and analysis that a lot of STEM undergrads don't even really get a whiff of except maybe knowing it's often said to be a thing.)

To try and be more helpful, I'll suggest you don't actually want to learn math at all. So don't! At least, not directly. Instead, find something you want to learn more about in science, engineering, or technology/programming, and dig into it until you start hitting the math being used. For many things, especially at the introductory level, it's fundamentally no more complicated than being able to read a junior-high-school level equation. Occasionally you'll need to know about some functions like square root, or sine, or exponentiation, or some other new functions that will be explained (like a dot product) in terms of those things. When you don't understand something, you may need to find an outside reference (or a few) for it, if the book itself doesn't cover it enough or to your liking. Even then, you can often find outside presentations of that thing which are still motivated by the general field and are thus not proof-heavy.

However sometimes the best explanation may still be found in a "pure" book just about the thing, and if you can get over whatever problem you have with proofs you can learn to see how they can be used to build your understanding of the thing in smaller pieces, not just as tools to say whether this or that is true or false. In other words, proofs can serve the same function as repetitive problem-solving exercises, and are often given as exercises for that reason.

I'm a fan of the Schaum's Outlines series of books just for the sheer amount of exercises available in them, I just wish I had better self-discipline to actually do more exercises. Though they maybe aren't the best resources for a brand-new introduction to something.

To give a small example, maybe you're interested in game programming, and eventually want to dive into studying 2D collision detection more specifically so you can implement it yourself instead of using someone else's library, so you might stumble on a copy of "2D Game Collision Detection: An introduction to clashing geometry in games". Its explanation of the dot product comes early (its whole first chapter is on basic 2D vectors), consisting of 2 diagrams and two code examples (the first mostly defining dot_product(), the second using it as part of a new enclosed_angle() function) and some text all over 2.5 pages. It gives things in programming notation instead of mathematical notation, apart from some ² squared symbols occasionally. It gives a few equivalences like a vector's dot product with itself is its length squared, shown as dot_product(v, v) = v.x² + v.y² = length², without proving them, and points you to wikipedia of all places if you want to know more about how that or another detail are true. Why learn it? It's used immediately after in explaining projection, and then later in collision detection functions. Generally that book is structured as: learn the bare minimum of vectors, use them to implement collision detection for lines, circles, and rectangles.

I'm not saying this is a great book but it's representative of what you'll find that I think you're really after, which is motivated use of some bits of math. If you don't like that book's treatment of vectors, there are a billion other game programming books that cover the same thing as a sub-detail of their main topic, and maybe even better for you because it'd be grounded in e.g. a graphical application you've already got setup and running to see results rather than a standalone library. Or there's special dedicated math books like "Essential Mathematics for Games and Interactive Applications". Or you can go find dedicated "pure math" books on linear algebra if you want. Or maybe your junior high / high school math education was good enough you can more or less skip most of this and move on to something more interesting, like physically based rendering (https://www.pbr-book.org/) which also of course has vectors and dot products with brief explanations. Or maybe you don't care at all about game programming, and want to learn about chemical engineering, or economics, or the mechanics of strength and why things don't fall down, or...