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Dear Hunter,
Thanks for your updates and your videos and I have checked the video you provided here again.
In your environment, the primary Title column is TitleParent?. The other two columns Title (Link to items with edit menu) and Title (Link to items) are linked to TitleParent?. So if you change the name of TitleParent?, the names of the two columns will also be changed to TitleParent?. The values of the two columns are changed based on the values of TitleParent? as well. The two columns are created by SharePoint Online by default and can't be deleted and can only be hiden. They are shown in the classic Edit Column UI and will not be shown in the modern Edit Column UI.
By defalt, SharePoint Online hides the primary Title column which is a single-line text column and show the Title (Link to items with edit menu) column linked to the primary column in the list after you create a new list. But the primary column is showed in the list edit form for you to add values on Title.
So you just need to rename TitleParent? to Title in your list and only leave Title (Link to items with edit menu) in the classic Edit Column UI to see if the issue can be fixed in your environment.
Thanks for your effort and time.
Cliff