[constants] Remove deprecated constants

[aleqsio]

Why

Suggested by @tsapeta, we have a whole host of deprecated properties from expo-constants that we can remove at this point.

One exception is the manifest field, that is still used by expo-constants JS code, so we keep it in native code and types, but we hide in the docs.

It can conflict with #26313, so let's wait with merging this PR until that one is merged.
CC @wschurman

Test Plan

Tested in bare-expo.

Checklist

• Documentation is up to date to reflect these changes (eg: https://docs.expo.dev and README.md).
• Conforms with the Documentation Writing Style Guide
• This diff will work correctly for npx expo prebuild & EAS Build (eg: updated a module plugin).

[wschurman]

Only change before commit is to revert the removal of manifest field and optionally remove the warning as noted inline. Other than that, this looks great!

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