Import the p12 Certificate from App Store Connect by Dragging and Dropping into Keychain Access.

When you change your Mac model, for example, and need to export the Apple Developer certificate in p12 format from the old Mac and import it to the new Mac, make sure to import it into the "Login" keychain, not the "System" keychain. Open the Keychain Access app and, with the "Login" keychain open, drag and drop the file into that window using your mouse. Do not install it by double-clicking.

Failure Experience

When I double-clicked the p12 file, it got installed into the System keychain.

If the certificate is installed in the System keychain, Xcode will repeatedly prompt you to enter the keychain password when you upload the archive built with Xcode to App Store Connect. Additionally, the "Always Trust" button will not be displayed.

It seems that the "Always Trust" option does not appear if it's in the System keychain. Therefore, open the "Login" keychain and drag and drop the certificate there.