Add to backend.run migration guide for 3rd party provider

[jyu00]

URL, if applicable

https://docs.quantum.ibm.com/migration-guides/qiskit-runtime

Describe the new content you are requesting.

Prompted by #2496 (comment), it'd be great to have a section on Migrate from third party provider under Migrate from backend.run to primitives to show people how to migrate to primitives even if the 3rd party provider they use don't support primitives (i.e. via backend primitives). This would allow users to switch between Qiskit Runtime and other 3rd party providers with little code modification.

If this new content request is accepted, do you want to write the content?

I can help the team by providing enough information to write the material

[jyu00]

Because I'm too lazy to open another issue, it'd be great to also add the motivation behind the move to primitives (also described in #2496) to the overview page.

[Eric-Arellano]

closing in favor of #2469

[jyu00]

@Eric-Arellano I think this issue is different from #2469. This one is about updating the content of the existing migration guide related to 3rd party provider (target audience being regular users). #2469 is about creating a new migration guide for 3rd party providers (target audience being providers). Sure you can do both in a single PR, but they don't have to be.

[beckykd]

I think this is all addressed in #2496