Hmm. I get where you're coming from. I'm quite crafty, but like you if I reflect on what I actually make, I don't make truly creative things, but I do have a flair.
I think you can develop it, but it takes work. And I don't think it's the same as being naturally creative. I think that's a different way of thinking entirely that's locked to me. But then the naturally creative probably would find a more linear way of thinking hard to comprehend.
To start with, perhaps, it's taking creative liberties with the instructions. Adding a border to cross stitch or different to the pattern, choosing a different wool colour or adding short sleeves instead of long to crochet. I realise these are instructions in and of themselves but they're a step in designing something.
Some crafts are more open to inspiration than others. Card making can be rigidly instructional I imagine, but once you have the idea you can create pieces following your own pattern as such.
I have a bullet journal. Which really is an excuse to doodle and spend a fortune on stationery. I spend a lot of time on pinterest. While I look at lot of others ideas, I don't copy, rather take elements I like and combine with others. It's hard to explain.
Also, apologies if this comes out rude and stupid, I don't mean it it way.
Have you ever just tried - as in got some paints out, or clay, or pencils and just played around to see what you make. Whatever came in that moment? Sometimes we think that what we make has to be good, otherwise we're not creative. If inspiration takes you to mould a rabbit with a carrot, it has to look like it. But it doesn't, you were still creating it, even if you didn't have the skills to implement it well.
Whether you choose the medium and await the idea, or you wait for the idea then choose the medium, I think is tricky.
True inspiration, I expect the idea influences the medium, but ultimately I think the more you use a medium, the more inspiration comes wanting to be expressed in that medium. Eg. If you're a model maker, with an idea for a train station, you're more likely to pick up the wood and glue, with some quick sketches than if you were a drawer, where you'd get your pencils out.