Add missing required transitive dependencies

Declare the transitive dependencies that our code already imports as
de facto dependencies in our `package.json`. Update the
`package-lock.json` accordingly.

For `@opentelemetry/instrumentation`, which is only required for a
type annotation, use `import type` instead.

.changesets/improve-compatibility-with-alternative-package-managers.md

@@ -0,0 +1,6 @@
+---
+bump: "patch"
+type: "fix"
+---
+
+Improve compatibility with alternative package managers. Fix an issue where AppSignal would fail to install with Yarn when using package managers that require transitive dependencies to be declared.