Hi Geoff and Eric,
Thanks for taking to help out with my issue, however it seems that my team has already found a way to resolve it!
I did try to do as both of you suggested, which was adding the "Pooling=False" to the connection string, which sadly didn't work, and there was nothing additional to note when looking in the Windows Event Viewer either. However, my team has provided a suggestion to use a service name instead of an SID in the connection string, and the bots are finally able to connect to the production database.
Once again, thank you for taking the time to answer my questions.
Best regards,
Caitlin