[build_test] update dependencies, prepare v2.2.2 release

[kevmoo]

Also bumped deps in example

[github-actions]

Package publishing

Package	Version	Status	Publish tag (post-merge)
package:build_test	2.2.2	ready to publish	build_test-v2.2.2
package:build_runner	2.4.8-wip	WIP (no publish necessary)
package:scratch_space	1.0.3-wip	WIP (no publish necessary)
package:build	2.4.2-wip	WIP (no publish necessary)
package:build_config	1.1.2-wip	WIP (no publish necessary)
package:build_daemon	4.0.1	already published at pub.dev
package:build_runner_core	7.2.12-wip	WIP (no publish necessary)
package:build_web_compilers	4.0.7	already published at pub.dev
package:build_modules	5.0.5	already published at pub.dev
package:build_resolvers	2.4.2	already published at pub.dev

Documentation at https://github.com/dart-lang/ecosystem/wiki/Publishing-automation.

[kevmoo]

landing w/ red markdown issue