I'm looking to get my hook grip developed to the point where I can lift with it without pain/injury. I'm also concerned about the impact that hook grip may have on my ability to play piano/keyboard. Any advice?
Slowly. Do hook grip on your first set for a week, and regular grip for your remaining sets. Then do hook grip on your first two sets for a week. Then your first three sets for a week, and so on. It helps if you have a ramp up routine (start with lower weights until you get to your working set) because you can do this scheme with lower weight and build up.
Hook grip will initially feel really weird. It should feel more natural in every set after a few weeks.
If your thumbs feel a little burnt, then simply don't do hook grip for one or two workouts then go back on the plan when they heal. There's no reason to torture yourself by pushing through pain.
As far as the piano concern... I can't speak to that. Anecdotally, hook grip will create slight calluses on your thumbs. It might make your thumb a little stiffer and harder to move (very slightly). I wouldn't expect it to significantly impact playing piano (my typing speed hasn't gone down any). Initially, your thumbs may feel like they're burning or sore immediately following a workout which will impact playing. Though that shouldn't be a concern once you're acquainted with it.
In addition to the other answer I would just add: use tape!
You can employ this when getting used to hook grip, but I've also seen elite folks continuing to use it. For me it not only helps with comfort but I think it improves the strength of my hookgrip a bit.
Not just any tape. Use stretchy, self-adhesive sports tape. This type of tape is flexible and sticks to itself, not you. Regular sports tape can actually make things much worse. Here is an example, but it's available in most any sporting good store. https://www.amazon.com/dp/B07TTGCZGC/ref=cm_sw_r_tw_dp_U_x_HsBkEb8RAD373
Use it sparingly. You don't want to overdue it and add bulk to your thumb. Get the 2inch roll and go around your thumb about 1.5 times.