[turbopack] Remove uses of `Value<ClientContextType>` by making `ClientContextType` a TaskInput (#80127)
Refactor ClientContextType to use TaskInput instead of Value wrapper
### Why?
The `Value<>` type is confusing and error prone, lets destroy it!
As discussed over slack, `turbo_tasks::Value` type always implements `is_resolved` as `true` and `is_transient` as `false` which is incorrect and can enable smuggling transient vcs into turbo tasks.
• https://vercel.slack.com/archives/C03EWR7LGEN/p1743456121241529
• https://vercel.slack.com/archives/C04NGV98TPS/p1743455453764879