Reverts "Write an identical value to bin/cache/engine.stamp to prepare for migration (#164317)" (#164396)

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Reverts: flutter/flutter#164317
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Initiated by: matanlurey
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Reason for reverting: `bin/cache` does not exist on a fresh checkout,
and `echo bin/cache/...` will fail as a result.

This blocked the google3 roll, but would also break new checkouts of
Flutter, for regular users/contributors.
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Original PR Author: matanlurey
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Reviewed By: {jtmcdole}
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This change reverts the following previous change:
Towards https://github.com/flutter/flutter/issues/164315.

This PR just writes `bin/cache/engine.stamp` identically to how
`bin/internal/engine.version` would otherwise be written, with a caveat
that _if_ `engine.version` is tracked, it is now _copied_ to
`bin/cache/engine.stamp`.

After this lands, I'll send PRs to update tooling that looks for
`engine.version` and give a heads up to the larger team (i.e. Dart HH
bot or whomever we will break by doing this).
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Co-authored-by: auto-submit[bot] <flutter-engprod-team@google.com>

.gitignore

@@ -1,6 +1,9 @@
 # Do not remove or rename entries in this file, only add new ones
 # See https://github.com/flutter/flutter/issues/128635 for more context.
 
+# This is dynamic in a monorepo
+bin/internal/engine.version
+
 # Miscellaneous
 *.class
 *.lock
@@ -30,8 +33,6 @@
 /bin/cache/
 /bin/internal/bootstrap.bat
 /bin/internal/bootstrap.sh
-/bin/internal/engine.realm
-/bin/internal/engine.version
 /bin/mingit/
 /dev/benchmarks/mega_gallery/
 /dev/bots/.recipe_deps