feat: upgrade API runtime dependencies

[hrodmn]

⚠️ Checklist if your PR is changing anything else than documentation

• Posted the link to a successful manually triggered deployment workflow (successful including the resources destruction) https://github.com/developmentseed/eoapi-cdk/actions/runs/26534722078/job/78160449852

Merge request description

Run uv sync --upgrade in all of the runtime directories to upgrade all dependencies.

Upgrading starlette and fastapi required some changes to the handler functions. Since I was working on that I unpinned us from mangum==0.19.0 so now we can stay up to date with new versions.

I also upgraded stac-auth-proxy to v1.1.1 to incorporate some security updates (supersedes #263).

[gadomski]

👍🏼 to allowing mangum version to float. It does feel like we're duplicating a lot of kinda complex code — is there any path to DRY-ing it up?

[hrodmn]

👍🏼 to allowing mangum version to float. It does feel like we're duplicating a lot of kinda complex code — is there any path to DRY-ing it up?

We have a mechanism for doing that already in utils.py - I'll check to see if any of the common functions could just be defined there and imported in each handler.