Overhaul update_engine_version.{sh|ps1} to reflect the new computation flow (#164513)

Closes https://github.com/flutter/flutter/issues/164030.
Closes https://github.com/flutter/flutter/issues/164315.
Towards https://github.com/flutter/flutter/issues/163896.

Significantly simplified! We removed:

- Conditional checks for monorepo (it's always a monorepo)
- Conditional checks for `LUCI_CONTEXT` (LUCI takes care of itself now,
see https://github.com/flutter/cocoon/pull/4261)
- ... and made the branching logic easier to follow as a result

You can see the results first hand in the tests, which are now much
simpler.

Canonical docs:
https://github.com/flutter/flutter/blob/master/docs/tool/Engine-artifacts.md.

.gitignore

@@ -26,12 +26,21 @@
 .vscode/*
 .ccls-cache
 
+# This file, on the master branch, should never exist or be checked-in.
+#
+# On a *final* release branch, that is, what will ship to stable or beta, the
+# file can be force added (git add --force) and checked-in in order to effectively
+# "pin" the engine artifact version so the flutter tool does not need to use git
+# to determine the engine artifacts.
+#
+# See https://github.com/flutter/flutter/blob/main/docs/tool/Engine-artifacts.md.
+/bin/internal/engine.version
+
 # Flutter repo-specific
 /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