1x11 on a budget with hydro upgrade.

Shimano RS505 shifters with flat mount calipers - $170
Shimano GRX812 rear derailleur - $110
Shimano GRX-RX600 crank - $140
Shimano Deore XT 11-42 cassette - $60
Total - $480

Now that is assuming you are paying full retail for the GRX bits which most places will have a 15-20% coupon so it can be cheaper.

2x9 is still HG so you can use an 11sp MTB cassette no problem.