Minimize shared-common everywhere (#188606)

## Summary


![8xfggo](https://github.com/user-attachments/assets/f3d9312f-2ad3-4fa2-9daf-01e2b1ad6cac)

At the moment, our package generator creates all packages with the type
`shared-common`. This means that we cannot enforce boundaries between
server-side-only code and the browser, and vice-versa.

- [x] I started fixing `packages/core/*`
- [x] It took me to fixing `src/core/` type to be identified by the
`plugin` pattern (`public` and `server` directories) vs. a package
(either common, or single-scoped)
- [x] Unsurprisingly, this extended to packages importing core packages
hitting the boundaries eslint rules. And other packages importing the
latter.
- [x] Also a bunch of `common` logic that shouldn't be so _common_ 🙃 

### For maintainers

- [x] This was checked for breaking API changes and was [labeled
appropriately](https://www.elastic.co/guide/en/kibana/master/contributing.html#kibana-release-notes-process)

---------

Co-authored-by: kibanamachine <42973632+kibanamachine@users.noreply.github.com>

scripts/saved_objs_info.js

@@ -7,4 +7,4 @@
  */
 
 require('../src/setup_node_env');
-require('../test/common/services/saved_object_info').runSavedObjInfoSvc();
+require('@kbn/test-suites-src/common/services/saved_object_info').runSavedObjInfoSvc();