[FEATURE]: Copy models into Recent/Favourites instead of moving

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

Currently, when you have used a model recently or have it as a favourite, it no longer appears under its associated provider. This is a visibility problem, as it makes it difficult for a user to see the full list of a provider's models in one place. Below is how users are currently forced to get this information and why this change is an improvement:

• For default providers, the user must extract the models that exist from Favourites, Recent and the provider's section.
• For custom providers, the user can also look at the config for models, but this is still not ideal.