[keyserver] Clean up run-prod.sh using ShellCheck

Summary: Related Linear issue here. This is part of a set of diffs that will allow ShellCheck to be added to the CI. See inline comments for specific details of the ShellCheck error/warning output.

Test Plan:
ShellCheck.

Additionally, this script is run during the keyserver build so if that workflow continues to pass CI we can reasonably assume that the script continues to work as expected.

Reviewers: atul, jon, tomek, ashoat

Reviewed By: atul, ashoat

Subscribers: adrian

Differential Revision: https://phab.comm.dev/D4712