Steps to reproduce multiple issues:

1. Have yarn 1.22.0
2. Have rush 5.20.0
3. Run rush update
4. All works as expected (check node_modules of all packages)
5. Go to already-added module and add @types/lodash into dependencies
6. rush update (check node_modules of already-added)
7. Works as expected, @types/lodash is added
8. Remove @types/lodash from package.json
9. rush update
10. It stays in node_modules
11. rush update --full
12. It's gone. Good.
13. Go add add-me to dependencies of add-to-me
14. Run rush update
15. Check node_modules of add-to-me there is NO add-me package added. (same applies to rush-link.json)
16. Run rush update --full
17. Nothing changed, same issue.
18. Add @types/lodash to add-to-me into dependencies
19. Run rush update (check node_modules of add-to-me)
20. @types/lodash is not added to node_modules nor to yarn.lock
21. Run rush update --full
22. Nothing changed. @types/lodash is not added to node_modules nor to yarn.lock
23. Add @types/node to already-added into dependencies
24. Run rush update (check node_modules of already-added)
25. For some weird reason @types/lodash is added instead of @types/node
26. Run rush update --full (check node_modules of already-added)
27. @types folder got removed completely.
28. Add @types/lodash to already-added into dependencies
29. Run rush update --full (check node_modules of already-added)
30. Same, nothing changed. Only lodash stays there. Meanwhile yarn.lock is untouched since our first update
31. Add @types/uuid to already-added to devDependencies and run rush update
32. It detects that something is have to be added! And adds only @types/lodash and nothing else.

Any manual deletion of yarn.lock of rush-link.json + rush update, or whatever commands like unlink link doesn't fix the issue Only rush update --full --purge fixes it all. But it's too long for real projects to make this all the time.