Being the reserve currency props up our currency conversions because everyone wants USD to trade with. If we lose that, the value of the USD falls relative to other currencies (and especially relative to the new reserve currency). Our GDP would presumably be measured in whatever the new reserve currency is, and that alone would cause a GDP drop just due to unfavorable currency conversions.

Being the reserve currency also makes imports cheap but exports unappealingly expensive. Losing that means the inverse; imports are expensive and exports are more appealing internationally, but our economy is set up for cheap imports and not exporting much. It would take a while to realign to doing manufacturing for domestic supply and GDP via exports.