Hi @sestillings , I am not sure we are talking bout the same thing (although we may be). Let me further explain ...
Here is your image:

This condition is looking for the "When a file is created (properties only)" Name paramater ... is that correct?
If so, your file, and there is only one that has been processed by the condition is called:
You have also posted this ...
The yes branch hasn't run as the condition has returned false.
There is no mention of a file containing "*project alpha*" .
You say "however the reason this file was identified is because it's an attachment of the original email (which does contain the "project alpha" phrase.)"
I can see no file containing the phrase "project alpha" in the images you have provided and the Flow is triggered on one file only, the one called "IDEXX Midyear Report 2018_1507075478". Are you maybe saying the email has the phrase, in it's body or title perhaps?
maybe I am, missing something here ...
i.e, this Flow will not get as far "Get file properties" or "Delete file" with the condition returning true?
You say "The core issue is that the file that did successfully copy with the "project alpha" phrase did not end up deleting. Any thoughts?" ... Have you maybe posted screen shots of a Flow run for a diferent file name? if so, maybe post the run that shows the successful copy & the delete with error to avoid the confusion. Post it's error and we can better advise.
Lastly, In your first image showing the delete ... you are using "Identifier" ... Is that from the Trigger "When a file is created (properties only)", or the Action, "Copy file" as it may just be this that is the issue but I can't tell from your images which you are using so if you can advise on that it may help us get closer to a resolution.
If you have found my post helpful, please mark thumbs up.
Any other questions, just ask.
Thanks, Alan