chore(mcp): convert lib/local-branch to TypeScript

Phase 2 of the packages/loopover-mcp TypeScript migration (#7291), building
on the tsc build pipeline from Phase 1 (#7409). Port lib/local-branch.js to
lib/local-branch.ts; it compiles in place to lib/local-branch.js (inline
source map, no .d.ts), the same file set the package already ships.

Runtime behavior and the public export surface are unchanged: every exported
function keeps its name and semantics, and bin/loopover-mcp.js consumes the
compiled .js exactly as before. Types are added at the git-diff/JSON/scorer
boundaries as open records, matching the already-converted lib/ files.

Closes #7329

Author: lourincedaging0-commits