[task] Resolve current GitHub repository

[phongndo]

Goal

Resolve the current GitHub repository from a local checkout so app-server methods know which repository they are reading.

Why this matters

TUI and desktop views need a clear repository context before showing issues, PRs, checks, and reviews. Nexgit should make the target explicit instead of relying on ambiguous defaults.

Command/API target

Add shared logic that can identify OWNER/REPO from the current working directory and Git remotes, with GitHub as the only MVP provider.

Depends on

• [task] Add GitHub API adapter using gh api #4 for the GitHub adapter pattern.

Out of scope

• Do not support GitLab, Codeberg, or Forgejo yet.
• Do not implement write-target safety or mutation prompts here.
• Do not add TUI or desktop rendering in this issue.

Definition of done

• A GitHub remote resolves to an OWNER/REPO value.
• Missing, non-GitHub, and ambiguous remotes produce understandable errors.
• The behavior is reusable by app-server methods.

Verification

• cargo fmt --all --check
• cargo check --workspace
• Tests cover GitHub remote, no remote, and unsupported remote cases.

Contributor notes

Keep this narrow. This is repository identity only, not issue or PR lookup.