Finding a good doctor would be the ideal course of action.
A rheuma isn’t a kindey specialist and no responsible doctor would use bullshit excuses to get rid of problem patients and let them fend for themselves.
I must have seen about a dozen doctors over the years. Most were useless and some were dangerous quacks. And I still had to do some of the work myself or I might have ended up without a solution. So don’t give up after the first couple of doctors.
Supplements can be even more dangerous than drugs. People promote many quick fixes to the desperate online. The best of these are useless but harmless.
I wouldn’t even dare to recommend a diet based on the very limited information you have shared so far. I have no idea what your current diet looks like or if it changed since the UA tests you shared. Worse, I don’t know if you have health problems requiring a special diet. What if you have a cholesterol problem affecting your tachycardia instance? A diet which would be fine for someone else could easily be more dangerous than febuxostat for you.
If you can’t find a decent doctor, you’ll have to research the issues slowly and methodically. Question everything. Gout isn’t going to kill you anytime soon so you can afford to take your sweet time. Preventing worse kidney problems might be more urgent which is one more reason I’d start by looking into these kidney stones and your kidney function more generally.
There’s one bit of advice I think I can give right now because so far as I know it is pretty safe: make sure you drink the generally recommended amount of water and avoid any diuretics (including alcohol) unless a doctor told you it was important you take a diuretic drug (in that case, ask the doctor if there is an alternative).