I was reviewing some rules from Peter Westergaard's An Introduction to Tonal Theory. I am really only literate in the key of C major, and so I was notating one of Westergaard's example in MuseScore so that I could then transpose the example into the key of C in order to interpret it. I noticed, however, that MuseScore wasn't allowing me to spell one of the pitches the way it's shown in the text—please see the notes indicated with an arrow in the following images.
My confusion lies with the A-flat note indicated by the arrow in the second image. When attempting to lower this A-flat by a half step in MuseScore, it suggests a G instead. My question revolves around whether the accidental added by Westergaard transforms the repeated note into an A-flat or if it's interpreted as a flattened version of the A-flat note diatonic to the key, resulting in a G.
Despite my limited grasp of enharmonic spellings, I'm hoping to understand if this is a fundamental misunderstanding on my part or if there's a difference in presentation between the textbook and MuseScore.