This is general advice because I’m not too familiar with the SRAM product line.
Any SRAM brifter should work so long as the cable pull is the same (I believe SRAM uses the same pull for everything) and it has the same number of gears. The SRAM rival 22 should be the closest/identical match because it’s 11 gears in back as well. It’s 22 for two gears in front and eleven in back for a total of 22
As for the replacement process, you’ve got it pretty much spot on. You’ll likely want new cables and possibly bar tape, but that isn’t a strict requirement.
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Lmao. This is so unfortunate.