Upgrade to Postgres 16

[mbarton]

Closes #1119

No particular rush on this as Postgres 15 is supported until November 11, 2027. Upgrading would speed up our tests in CI though from 30 mins to 10 mins (see #1119).

I've tested locally and it all seems to work. However I don't think we should do this before the end of January 2025 as that's the data submission deadline for cohort 6 and we don't want any risk before then.

Postgres 17 was released in September 2024 and is still in preview on Azure (https://learn.microsoft.com/en-us/azure/postgresql/flexible-server/concepts-supported-versions). If it is out of preview by the time we get to this issue I would suggest we hop to 17, although that may mean longer downtime as you can only upgrade one major version at a time.