I wouldn't say that I'm actively looking for symbolism, but I do notice it, at least sometimes. I think if you've spent time learning about it, as you have, then you'll just notice it. Maybe not every time, but maybe people who are very actively looking for it are inventing it themselves sometimes too. With some authors, it's very obvious there's some symbolism going on - Murakami, Salman Rushdie, or J G Ballard for example.

Something that does help is to think about the purpose of everything in the writing. The author has chosen every word, and so think about why they've chosen to include each element. Is it just to set the scene and "world build"? Or does it connect to the narrative? The main character's mother has just got sick, and now we're being told about a tree they used to play on as a kid that's now lost all it's leaves? The author has made these connections deliberately.

If you're thinking about the purpose of each word, and element, just be aware that you don't need to come up with answers. Maybe it won't become clear until later, or maybe never. Just spending time thinking about why they've made the deliberate decision to include that element will be enough to build a better ability to see symbolism and metaphors in a book over time.