@Hunter K I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: You are looking to change the auto-pause delay for your Azure SQL database. and want to keep the database up during normal business hours and auto-pause at night. you have checked under "Compute + Storage" and scrolled to the bottom but cannot find any controls for this. and also noticed that the auto-pause delay is currently set to 1 hour based on the "Overview -> Properties" tab.
Solution: As you mentioned yes if you have the free-tier applied, the options to change the auto-pause delay may not be visible. In that case, you will need to toggle off the free-tier on the same page "Compute + Storage" to access the auto-pause delay option. Once the free-tier is toggled off, the option to change the auto-pause delay should appear.
If you have any other questions or are still running into more issues, please let us know. Thank you again for your time and patience throughout this issue.
Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.
Regards
Geetha