Fix master channel build (#1900)

- Fixes #1899 - Don't use BuildContext in async.
- Disabled build script for `next-gen-ui-demo` for master channel
because dependency gap does not compile.
- Improve use BuildContext in `place_tracker`, added checks to verify
that the context is still mounted, and avoid passing BuildContext as
parameter.

## Pre-launch Checklist

- [ ] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [ ] I signed the [CLA].
- [ ] I read the [Contributors Guide].
- [ ] I updated/added relevant documentation (doc comments with `///`).
- [ ] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-devrel
channel on [Discord].

<!-- Links -->
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[CLA]: https://cla.developers.google.com/
[Discord]: https://github.com/flutter/flutter/wiki/Chat
[Contributors Guide]:
https://github.com/flutter/samples/blob/main/CONTRIBUTING.md

tool/flutter_ci_script_master.sh

@@ -53,7 +53,8 @@ declare -ar PROJECT_NAMES=(
     "material_3_demo"
     # TODO(DomesticMouse): The '!' will have no effect because the receiver can't be null.
     # "navigation_and_routing"
-    "next_gen_ui_demo"
+    # TODO: Dependency 'gap-3.0.0' fails to compile
+    # "next_gen_ui_demo"
     "place_tracker"
     # TODO: https://github.com/flutter/samples/issues/1765
     # "platform_channels"