[Feature]: merge button on ready-to-merge PR cards

[dimkah]

Problem

AO takes a session all the way through the lifecycle — working → in review →
ready to merge — and notifies me when CI is green and the PR is mergeable.
But the final step breaks the flow: the PR card only offers a link to GitHub
("one click to the PR"), so the one remaining human action (the merge itself)
requires leaving the app.

Given AO's philosophy of "human steps in at PR time", the PR card is exactly
where that step should be possible.

Proposed direction

A "Merge" button on the PR card / session inspector when the PR state is
ready-to-merge (checks green, approvals satisfied, no conflicts):

• executes merge via the existing gh integration (AO already acts "as you")
• respects repo merge settings; ideally a small dropdown for
  merge / squash / rebase, or just default to the repo's allowed method
• disabled with a tooltip when branch protection blocks merging
• after merge: card transitions to done, worktree cleanup follows the
  existing post-merge flow

Alternatives considered

• gh pr merge in the session terminal — works, but defeats the purpose of
  the board as mission control
• GitHub auto-merge — good for full automation, but not for the
  "review, then consciously press merge" workflow AO is designed around

Before submitting

• I searched existing issues / discussions for something similar
• I am willing to help implement this if maintainers agree on scope

[somewherelostt]

Thanks for contributing to Agent Orchestrator.

This issue is being picked up by the current external contributor on-call pair:

• @illegalcall
• @Pulkit7070

If someone is already working on this, please continue as usual.
The on-call pair is added for visibility, tracking, and support, not to take over the work.
If you need help with review, direction, reproduction, or next steps, please tag @illegalcall and @Pulkit7070 here.

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[shubham-shinde-442]

@illegalcall Want to work on this.