Xcode – MobileDevice.pkg untrusted, cannot open Xcode after OS X update

After an automatic update of macOS v10.15 (Catalina), I am unable to open Xcode. Xcode prompts me to install additional components but the installation fails because of MobileDevice.pkg (Applications/Xcode.app/Contents/Resources/Packages)

I have found multiple answers on how to locate MobileDevice.pkg and that I should try to install it directly, but when I try to do this the installation fails too. I have also tried updating Xcode from App Store, but the update failed when it was nearly finished.

Has anyone experienced the same behaviour? Should I reset the Mac to default and install macOS v10.13 (High Sierra) or Catalina from scratch or it is a problem of Xcode and re-install would do the job?

I have found a discussion here that was posted today and is probably regarding the same issue and it seems like many people are dealing with it, too.

The log:

*2019-10-25 01:03:34+02 Vendula-MacBook-Pro Xcode[1567]: Package: PKLeopardPackage 
<id=com.apple.pkg.MobileDevice, version=4.0.0.0.1.1567124787, url=file:///Applications/Xcode.app/Contents/Resources/Packages/MobileDevice.pkg> 
Failed to verify with error: Error Domain=PKInstallErrorDomain Code=102 
"The package “MobileDevice.pkg” is untrusted." 
UserInfo={
  NSLocalizedDescription=The package “MobileDevice.pkg” is untrusted., 
  NSURL=MobileDevice.pkg -- file:///Applications/Xcode.app/Contents/Resources/Packages/, 
  PKInstallPackageIdentifier=com.apple.pkg.MobileDevice, 
  NSUnderlyingError=0x7fabf6626d00 
  {
    Error Domain=NSOSStatusErrorDomain 
    Code=-2147409654 "CSSMERR_TP_CERT_EXPIRED" 
    UserInfo={
      SecTrustResult=5, 
      PKTrustLevel=PKTrustLevelExpiredCertificate,   
      NSLocalizedFailureReason=CSSMERR_TP_CERT_EXPIRED
    }
  }
}*