That doesn’t mean it won’t matter to any other faculty member at any other program. I suppose if one weren’t to mention they were a PhD student, it couldn’t be an issue unless mentioned in a reference letter or call. However, I’ve seen a peer struggle with interview questions at some - certainly not all - institutions they interviewed at because they did share that they were a PhD student who hadn’t found the right fit and so chose to master out. This led to several follow up questions they weren’t expecting to clarify what happened. Not all faculty will be so open minded or objective.
It might look like just a masters on a CV, but I wouldn’t recommend going to any lengths to pretend that’s all it was if relevant questions arise. It might not be a big deal in most cases, but my point was that in this case it sounds like the OP wanted to use PhD funding to get a masters degree and then trade up. Maybe the new faculty wouldn’t care, but some might question the ethical nature of the student if this were to be suspected. OP avoided the need to find more adequate explanations or put on an act if the need arose.