Replace deprecated 'echo "::set-output name=...' syntax with new 'echo
"<name>=<value>" >>$GITHUB_OUTPUT' syntax [1], clearing the deprecation
warning appearing in the 'release-homebrew.yml' workflow.

[1] https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

Replace deprecated 'echo "::set-output name=...' syntax with new 'echo
"<name>=<value>" >>$GITHUB_OUTPUT' syntax [1]. A second fixup patch will
remove the one remaining instance of the old syntax to clear the deprecation
warning in 'build-git-installers.yml'.

[1] https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

Finish replacing deprecated 'echo "::set-output name=...' syntax with new
'echo "<name>=<value>" >>$GITHUB_OUTPUT' syntax [1], clearing the
deprecation warning appearing in the 'build-git-installers.yml' workflow.

[1] https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

Update 'actions/checkout' to v3 to stop using a deprecated Node.js 12
version of the action.

Update 'actions/checkout' to v3 to stop using a deprecated Node.js 12
version of the action.

Update 'actions/checkout' to v3 to stop using a deprecated Node.js 12
version of the action.

Update 'actions/checkout' to v3 to stop using a deprecated Node.js 12
version of the action.

Update 'actions/checkout' to v3 to stop using a deprecated Node.js 12
version of the action.

Upgrade 'actions/github-script' from v4 to v6 to silence the Node.js 12
deprecation warning. Note that this also includes an update to how the
'github' object is accessed in the script ('github' -> 'github.rest') due to
a breaking change introduced in v5 [1].

[1] https://github.com/actions/github-script#breaking-changes-in-v5

Upgrade the 'actions/setup-dotnet' Action to v3 to stop using Node.js 12
(deprecated).

Signed-off-by: Victoria Dye <vdye@github.com>

Upgrade the 'actions/upload-artifact' Action to v3 to stop using Node.js 12
(deprecated).

Signed-off-by: Victoria Dye <vdye@github.com>

Update to Node.js 16 versions of 'mjcheetham/asset-hash' [1] and
'mjcheetham/update-homebrew' [2].

[1] mjcheetham/asset-hash#342
[2] mjcheetham/update-homebrew#17

Update the runner versions for the Scalar Functional tests to supported
versions. For MacOS, update to the main supported version (macos-11). For
Ubuntu, ensure we're still testing the two latest LTS versions by replacing
18.04 with 22.04.

Also update the installed dotnet version to the latest v3.1 patch version.

Signed-off-by: Victoria Dye <vdye@github.com>