Roll Flutter Engine from 49d3ce9c2ae3 to 406f0c477afb (5 revisions) (#137720)

https://github.com/flutter/engine/compare/49d3ce9c2ae3...406f0c477afb

2023-11-01 skia-flutter-autoroll@skia.org Roll Skia from 84e1dc3af49e to 613abdf2c895 (4 revisions) (flutter/engine#47560)
2023-11-01 skia-flutter-autoroll@skia.org Roll Skia from 4594e2ef3ee8 to 84e1dc3af49e (1 revision) (flutter/engine#47558)
2023-11-01 jason-simmons@users.noreply.github.com Consolidate all the copies of the OpenFixtureAsSkData testing helper function (flutter/engine#47491)
2023-11-01 skia-flutter-autoroll@skia.org Roll Dart SDK from 15558b6ae7d5 to e6df03a57636 (1 revision) (flutter/engine#47556)
2023-11-01 skia-flutter-autoroll@skia.org Roll Skia from 816d41255105 to 4594e2ef3ee8 (1 revision) (flutter/engine#47555)

If this roll has caused a breakage, revert this CL and stop the roller
using the controls here:
https://autoroll.skia.org/r/flutter-engine-flutter-autoroll
Please CC rmistry@google.com,zra@google.com on the revert to ensure that a human
is aware of the problem.

To file a bug in Flutter: https://github.com/flutter/flutter/issues/new/choose

To report a problem with the AutoRoller itself, please file a bug:
https://issues.skia.org/issues/new?component=1389291&template=1850622

Documentation for the AutoRoller is here:
https://skia.googlesource.com/buildbot/+doc/main/autoroll/README.md

bin/internal/engine.version

-49d3ce9c2ae3a2e5721e9a40a9d1d7835bfb7e61
+406f0c477afb8b57caa24bd1040af5596815c2c6