Hi Jonah, good advice from Billy there. Like Billy, I can only offer from my own experience, which is limited compared to others here. However, like yourself I came from playing guitar onto steel and I have experienced what you are describing. Playing from tab is OK but improvising or making up your own parts is difficult.
I think the problem is partly that you/I still think in terms of playing guitar as opposed to playing steel, the solution is to think steel and not guitar, if that makes sense

As to how to get there, that is the hard bit. It depends on what you want to do with the steel, what style do you want to play, is it Country, Jazz, Rock etc.
I spent a good 3-4 months working through a Joe Wright tutorial exercise, which involved picking pattern exercises, where there were about 40 different exercises. Each exercise was a different picking pattern, from low to high strings and from high to low strings. I expanded this by starting on open fret, then moving up the fret board a fret at a time until I reached fret 24 and then worked my way back down again. I put aside 2-3 hours a night for around 3 months to get through it. Extremely boring at times, but at the end my bar positioning and picking technique was almost automatic. Committed to muscle memory if you like.
This in itself didn't teach me how to improvise etc, but it did make it a lot easier overall to play with confidence.
In addition to what Billy posted, learning harmony scales etc, which are extremely useful, it is good to learn the positions of the different inversions of chords. For example, no pedals/levers on fret 3 is essentially a G major, on fret 6 with A Pedal and F lever engaged is also a G major, fret 10 with A & B engaged is also a G major. Depending on where on the fret board you are moving from, a certain inversion might work better than another. If you are playing a D at fret 10, no pedals/levers, and the next chord is a G then the obvious inversion is fret 10 with A & B engaged. Alternatively, if you are playing the D on fret 5 with A & B engaged, then it is easier to play the G on fret 3 no pedals/levers or fret 6 with A Pedal and F lever engaged.
I find it useful to work through the inversions, so in G starting at fret 3, moving up to fret 6, then moving up to fret 10 and finally up to fret 15. It is useful as you get to know different ways to play the same thing.
Working out tab on popular songs can also be useful in expanding your vocabulary. For the past year I've been working on Forever Loving You, played on Pedal Steel by Tom Bromley. He makes it sound simple, but in reality it is a difficult piece to play. I can just about play the tab for it but getting the expression and feel that Tom puts into it is a different matter. However, I have learned a lot of moves from working away on it that I try and incorporate into my own bag of tricks, such as it is.
There are plenty of "lick" tutorials, where you can learn 'standard' runs, links, intros and outros from. These can sound a bit cheesy but often you can find some that you like and work for you that you can incorporate into your playing.
Of course the best thing is seat time, put on a basic backing track, say a typical 12 bar, and just play along with it, trying different things. Eventually you start to develop your own style etc.
As you will have discovered this is not an easy instrument to learn and it does take time, it did for me anyway. I was talking to my friend Calum recently and he told me he had reached a stage in his playing where he doesn't have to think much about what he's playing, it just kinda happens and that this change was almost overnight. It's like all the playing and practicing swirls around your subconscious and one day you wake up and it's all there at your fingertips.
It'll come, it can be frustrating getting there but as the saying goes - "“It's not the destination, it's the journey”.