Give it a couple days for 18.7.3 to show up (I’m trying this myself) or download the ipsw for ios 18.7.3 and use a computer to install.

I don't believe an IPSW for 18.7.3 was released except for devices that couldn't upgrade to iOS 26. I believe this is done to prevent downgrades.

Apple doesn’t provide IPSWs once the next major version has launched. OTA is the only option.

You can also join the iOS 18 public beta to get the update.

How do you do that? And do you need an AppleID to do so?

If you have the tolerance for betas, indeed

Someone above said that the 18.7.3 you can install as beta is in fact the production build. Disable beta access after that update.

Correct, both are the same build (22H217). BetaWiki has this build labeled as both the RC and the actual release: https://betawiki.net/wiki/IOS_18