This answer summarizes information from comments and outside sources, for preservation.
This appears to be a bug introduced in Visual Studio 2022 release 17.5.
I discovered that the 32-bit version of IIS Express Tray does not suffer from the same crash. Therefore, as a workaround, you can manually launch the 32-bit version of IISExpressTray.exe, typically under "C:\Program Files (x86)\IIS Express". IISExpressTray.exe will automatically recognize running IIS Express web processes regardless of their bitness. You don't need to switch to 32-bit web processes for this workaround.
The bug has been reported to Microsoft by another user here: https://developercommunity.visualstudio.com/t/iisexpress-crashes-in-ntdlldll/10290067
The poster of the bug report looked at a crash dump and discovered that the crash happened while processing telemetry data. Then they confirmed that deactivating participation in the Visual Studio Experience Improvement Program would work around the bug entirely.
To deactivate participation in the Visual Studio Experience Improvement Program: Open Visual Studio 2022. Go to Help
-> Privacy
-> Privacy Options...
. Then, near the bottom of the dialog, select "No, I would not like to participate". Please consider rejoining the program once the bug is fixed by Microsoft.
At the time of this writing the bug has been triaged but not yet resolved.
Update: Microsoft indicates that this issue was resolved in Release 17.5.4 (April 12 2023) (https://learn.microsoft.com/en-us/visualstudio/releases/2022/release-notes#17.5.4)