If you get the above cable hydro brakes. I’ve got a unused Sora groupset (without the cranks) you could have for not a lot of cash it previous gen doesn’t go under the bar tape.
You could do easy and within budget especially if you’ve got the brakes with a flat bar but then apparently it’s a hybrid not a gravel bike. You could stick micro shift or Deore on it, use cheap mtb crank with a nw chain ring of choice.
Ive also got some older 10 speed tiagra shifters a little battered that need new hoods, pair that with a 9 speed mountain bike mech you can get a 36t cassette on the back and probably bigger with a roadlink if you wanted to go single ring.
I don’t think you will get hydro and drop bar in your budget at the moment.