…ter (#13278)

* fix: use DeepPartialSkipArrayKey for WatchObserver value parameter

Fixes #13269

Changes WatchObserver type to use DeepPartialSkipArrayKey instead of
DeepPartial for the value parameter. This prevents unnecessary
undefined injection when field values are arrays, like multi-value
select inputs.

Before: (string | undefined)[] | undefined
After: string[] | undefined

This provides more accurate type inference without breaking changes,
as DeepPartialSkipArrayKey still handles optional fields correctly.

* Update API contract for WatchObserver type change

When clearErrors is called with specific field name(s), the state
emission now includes the 'name' property so that shouldSubscribeByName
can properly filter updates. This prevents components subscribed to
unrelated field names (with exact: true) from unnecessarily re-rendering.

Fixes #13277

Co-authored-by: Kai Gritun <kai@kaigritun.com>