Hello @Trent B and welcome to Microsoft Q&A.
I think I ran into a similar issue once before. In that case, I was using Postman for the call to get the token, then I used Postman for the data-bearing call. Then I tried the data-bearing call in ADF using the token obtained with Postman. Then the ADF call failed.
When I implemented the token-fetching call in ADF, and passed that token to the data-bearing call in ADF, it worked.
This lead me to believe there is an agent-dependent factor used by the server when the data-bearing call processes the token.
In the long run, it is better to implement the token-fetching call in ADF because the token eventually expires. Otherwise, when the token expires, you would need to manually update the pipeline with a new token.
Does this sound like your case?