I also don't particularly like the separate leveling of skills and stats, but I envisioned the combination differently...
Regarding classes – the variety does suffer. I suggest creating a system where you can take skills from other classes, but with limitations. For example, no more than one or two, or at a higher cost. Accordingly, for your "versatile" race, these limitations should be removed, partially or completely. Something like that.
And it would be good to add a few more skills to the existing system. I think so.