Add "Prove" button in Sidebar View

[Savio-Sou]

Problem

The Noir VS Code extension does not currently support proving Noir programs within the extension, which could be useful for Noir development workflows in e.g. in-browser VS Code.

Happy Case

As a Noir developer, I want to:

1. Type <my_desired_proof_name> in a field in the Noir Sidebar View
2. Click a "Prove" button in the View (which generates a proof of executing the Noir program with selected inputs named <my_desired_proof_name>)

so I can carry out further actions with the proof either in the View or elsewhere (e.g. verifying; exact actions would be covered in other GitHub Issues).

If there is a name clash of <my_desired_proof_name> with an existing proof previously generated and stored in the local instance, the extension should prompt me with an error and ask me to choose an alternative proof name.

Alternatives Considered

No response

Additional Context

No response

Would you like to submit a PR for this Issue?

No

Support Needs

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Pending

Beta Give feedback

1. Add Sidebar View #6
   enhancement +1
2. Add Noir program inputs section in Sidebar View #7
   0 of 1
   enhancement +1

[Savio-Sou]

Would this require an intermediate GitHub Issue for an "Execute" button?