feat: make worktree branch prefix configurable

[binbandit]

Summary

• add a persisted settings field for the worktree branch prefix, keeping t3code as the default
• thread the configured prefix through new worktree creation and cross-repo PR worktree preparation
• centralize branch-prefix normalization in shared git helpers and preserve the chosen prefix during first-turn auto-renames

Validation

• bun fmt
• bun lint
• bun typecheck
• bun run vitest run packages/shared/src/git.test.ts packages/contracts/src/git.test.ts apps/server/src/git/Layers/GitManager.test.ts apps/server/src/orchestration/Layers/ProviderCommandReactor.test.ts
• bun run vitest run apps/web/src/appSettings.test.ts apps/web/src/lib/gitReactQuery.test.ts

Note

Make worktree branch prefix configurable via app settings

• Introduces DEFAULT_WORKTREE_BRANCH_PREFIX (t3code) and shared utilities (normalizeWorktreeBranchPrefix, buildGeneratedWorktreeBranchName, resolvePullRequestWorktreeLocalBranchName) in packages/shared/src/git.ts to centralize branch naming logic.
• Adds a worktreeBranchPrefix field to app settings, normalized on save, so users can customize the prefix applied to temporary worktree and cross-repo PR branches.
• Exposes a Git section in the settings UI (apps/web/src/routes/_chat.settings.tsx) with an input, example output, and a reset-to-default button.
• Threads the configured prefix through ChatView, PullRequestThreadDialog, and preparePullRequestThread API contract so all branch creation paths use the user's prefix.
• Behavioral Change: existing worktree branches created with the old hardcoded prefix (t3code) remain unchanged, but new branches will use whatever prefix the user has configured.

^{Macroscope summarized 9b27f32.}

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