refactor: clean up remaining client type imports using backend types

[karrui]

Problem

This PR cleans up the remaining types on the client side that is still using backend types.

Note that deprecated types that will not follow us into React are left alone.
This is namely

• the old PublicFormUpdate DTO
• Examples related types, since that is going to be deprecated

This PR will complete #2066 once it is merged alongside with #2509

Solution

Breaking Changes

• Yes - this PR contains breaking changes
  • Details ...
• No - this PR is backwards compatible
  • Moving types only

Features:

• refactor: move src/types/api/auth to shared/types/form/form_auth

[mantariksh]

as discussed in #2355 (#2355 (comment), #2355 (comment)), do we need to clean up the aliases and exports as well?

[karrui]

as discussed in #2355 (#2355 (comment), #2355 (comment)), do we need to clean up the aliases and exports as well?

Yes, will be separate PR. I guess we can extend the scope of #2066 hahaha

[mantariksh]

ok approving on the basis that the additional cleanup will come separately