Cleans up header order/grouping for consistency: associated header, C/C++ system/standard library headers, library headers, platform-specific #includes.

Adds <cstring> where strlen, memcpy are being used: there are a bunch of places we use them transitively.

Applies linter-required cleanups. Disables linter on one file due to included RapidJson header. See https://github.com/flutter/flutter/issues/65676

This patch does not cover flutter/shell/platform/darwin. There's a separate, slightly more intensive cleanup for those in progress.