As @Keith30309 said, the authorization is typically “replaced” with the actual charge when it is settled. However, if the authorization was for incidentals and none were purchased, there won’t be a charge to settle. In my own experience with prepaid hotel bills and those paid with points the hotel closes the folio and within a few days the charge falls off, i.e. when the zero dollar amount transaction makes its way to the card issuer.
The idea of contacting the hotel requesting a temporary line increase is a good one. You might want to start with the dispute department and explain that you want either the line increase or the auth to be dropped. It sounds like this is your only card, so it wouldn’t hurt to remind them that you are a loyal cardholder who uses them as your exclusive credit provider. Then, apply for another card at a different bank. It doesn’t hurt to have a backup card. Also, it helps you gauge your bank’s service. You shouldn’t have to jump through these hoops.