"Unable to Check for Update" error while updating iPhone 13 Pro

Device: iPhone 13 Pro

iOS version: 18.0

While trying to check for updates, such error occurs:

"Unable to Check for Update. An error occurred while checking for a software update".

Exactly the same error as described here: If your iPhone or iPad won't update - Apple Support

I've already tried to:

1. Check Your Internet Connection: device is connected to a stable and reliable Wi-Fi network. Another device doesn't have such problems on the same Wi-Fi network. Private Wi-Fi address - I've tried all 3 options. Limit IP Address Tracking - tried both options. Doesn't help.
2. Try Cellular Data: doesn't help.
3. Restart Your Device: doesn't help.
4. Check Apple's Servers: servers work as expected.
5. Check Available Storage: there are 37GB of free space available.
6. Disable VPN or Proxy: it's disabled, doesn't help.
7. Date and Time Settings: it's verified to be correct.
8. Reset Network Settings: didn't help.
9. Try Later: didn't help for a few months, starting from release of the very next update > 18.0. Currently it's 18.2
10. Update via iTunes (if applicable): not applicable. Sequoia 15.2 doesn't show any connected device in Finder window. Finder is configured to show CD's, DVD's and iPods. Device is visible via Photos and Xcode app but those don't allow to install update to the iPhone.

Here is log message from Console app:

Preferences(SoftwareUpdateCoreSupport)
Subsystem: com.apple.su

[DIAG_ERROR] ANOMALY: [FSM] ACCEPT_EVENT, reason=FSM(SUSettingsScanOperation:18.0(22A3354,8EB0583D-3EE3-4FC8-91FD-561A1E0ECD10)) current state(Idle) does not support post event(ConcurrentActionFailed) result=8501

and/or after tap "Try again" button:

[DIAG_ERROR] ANOMALY: [SUSettingsScanOperation], reason=Scan FSM has reported an anomaly result=8116 error:SUCoreError(SUCore):kSUCoreErrorUnexpectedValue(8116) | [kSUCoreErrorUnexpectedValue] unknown action(ReportScanFailed)

googling for those errors brings to zero result. Does anyone know how to fix this and install update?

[Re-Titled by Moderator]