fix(worktree): disable automatic database backups (#10520)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work
> - Paperclip creates isolated instances for linked git worktrees so
development does not affect the primary instance
> - Those instances inherited the source instance's automatic
database-backup setting and also repaired older configs without
overriding it
> - As worktrees accumulated, each isolated instance could schedule its
own backup stream, producing redundant backup churn for disposable
database clones
> - This pull request makes backup disablement an invariant of worktree
config creation and repair
> - The benefit is that automatic backups remain focused on the durable
primary instance while isolated development instances stop accumulating
redundant backup files

## Linked Issues or Issue Description

No public GitHub issue exists for this bug, so the report is included
here. The closest related open change is Refs #10266, which hardens
where worktree config repair may write; this PR changes the backup
policy applied by that repair and by worktree initialization.

### What happened?

Isolated worktree instances copied `database.backup.enabled` from their
source config. When the source instance enabled automatic backups (the
normal default), every linked worktree also enabled a scheduled backup
stream. Existing worktree configs kept that state during startup repair,
so the redundant backups continued after the policy changed.

### Expected behavior

Automatic database backups are disabled for isolated worktree instances
created by `paperclipai worktree init` or `paperclipai worktree:make`,
and legacy worktree configs are migrated to that policy during normal
startup repair. The durable primary/default instance keeps its existing
backup behavior.

### Steps to reproduce

1. Start from a Paperclip instance whose database backup setting is
enabled.
2. Create or initialize a linked worktree with `paperclipai worktree
init`.
3. Inspect the generated worktree config and environment.
4. Before this change, the config retained `database.backup.enabled:
true` and the environment had no disabling override; after this change,
the config is false and `PAPERCLIP_DB_BACKUP_ENABLED=false` is
persisted.

### Paperclip version, deployment mode, and environment

- Reproduced against `master` before commit `ea5e0a0269`.
- Deployment mode: local trusted development with linked git worktrees
and embedded PostgreSQL.
- Environment: Node.js 22, pnpm workspace install.

## What Changed

- Always generate isolated worktree configs with automatic backups
disabled.
- Persist `PAPERCLIP_DB_BACKUP_ENABLED=false` in generated worktree
environments.
- Repair existing isolated worktree configs and environments that still
enable backups.
- Add CLI and server regression coverage for creation and legacy repair
paths.
- Document the worktree-specific backup policy and primary-instance
exception.

## Verification

- `pnpm exec vitest run cli/src/__tests__/worktree.test.ts
server/src/__tests__/worktree-config.test.ts` — 52 tests passed.
- `pnpm -r typecheck` — passed.
- `pnpm build` — passed.
- All repository commands above were run with inherited worktree runtime
identity variables removed.

## Risks

- Low operational risk: the change is limited to explicitly isolated
worktree instances.
- Operators who intentionally relied on automatic backups of disposable
worktree databases will now need to run a manual backup or explicitly
manage those files outside the scheduled worktree runtime.
- No schema, migration, API, UI, lockfile, or workflow changes.

> For core feature work, check [`ROADMAP.md`](ROADMAP.md) first and
discuss it in `#dev` before opening the PR. Feature PRs that overlap
with planned core work may need to be redirected — check the roadmap
first. See `CONTRIBUTING.md`.

## Model Used

- OpenAI Codex based on GPT-5 (the runtime does not expose a more
specific snapshot ID or context-window value), using reasoning, tool
use, local code execution, and GitHub CLI integration.

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [x] I have checked ROADMAP.md and confirmed this PR does not duplicate
planned core work
- [x] I have searched GitHub for duplicate or related PRs and linked
them above
- [x] I have either (a) linked existing issues with `Fixes: #` / `Closes
#` / `Refs #` OR (b) described the issue in-PR following the relevant
issue template
- [x] I have not referenced internal/instance-local Paperclip issues or
links (only public GitHub `#NNN` / `github.com/paperclipai/paperclip`
URLs)
- [x] My branch name describes the change (e.g. `docs/...`, `fix/...`)
and contains no internal Paperclip ticket id or instance-derived details
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] All Paperclip CI gates are green
- [x] Greptile is 5/5 with no open P2s, recommendations, or follow-ups
- [x] I will address all Greptile and reviewer comments before
requesting merge

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

cli/src/__tests__/worktree.test.ts

@@ -276,6 +276,7 @@ describe("worktree helpers", () => {
       path.resolve("/tmp/paperclip-worktrees", "instances", "feature-worktree-support", "db"),
     );
     expect(config.database.embeddedPostgresPort).toBe(54339);
+    expect(config.database.backup.enabled).toBe(false);
     expect(config.server.port).toBe(3110);
     expect(config.auth.publicBaseUrl).toBe("http://127.0.0.1:3110/");
     expect(config.storage.localDisk.baseDir).toBe(
@@ -289,6 +290,7 @@ describe("worktree helpers", () => {
     expect(env.PAPERCLIP_HOME).toBe(path.resolve("/tmp/paperclip-worktrees"));
     expect(env.PAPERCLIP_INSTANCE_ID).toBe("feature-worktree-support");
     expect(env.PAPERCLIP_IN_WORKTREE).toBe("true");
+    expect(env.PAPERCLIP_DB_BACKUP_ENABLED).toBe("false");
     expect(env.PAPERCLIP_WORKTREE_NAME).toBe("feature-worktree-support");
     expect(env.PAPERCLIP_WORKTREE_COLOR).toBe("#3abf7a");
     expect(formatShellExports(env)).toContain("export PAPERCLIP_INSTANCE_ID='feature-worktree-support'");

cli/src/commands/worktree-lib.ts

@@ -197,7 +197,7 @@ export function buildWorktreeConfig(input: {
       embeddedPostgresDataDir: paths.embeddedPostgresDataDir,
       embeddedPostgresPort: databasePort,
       backup: {
-        enabled: source?.database.backup.enabled ?? true,
+        enabled: false,
         intervalMinutes: source?.database.backup.intervalMinutes ?? 60,
         retentionDays: source?.database.backup.retentionDays ?? 30,
         dir: paths.backupDir,
@@ -258,6 +258,7 @@ export function buildWorktreeEnvEntries(
     PAPERCLIP_CONFIG: paths.configPath,
     PAPERCLIP_CONTEXT: paths.contextPath,
     PAPERCLIP_IN_WORKTREE: "true",
+    PAPERCLIP_DB_BACKUP_ENABLED: "false",
     ...(branding?.name ? { PAPERCLIP_WORKTREE_NAME: branding.name } : {}),
     ...(branding?.color ? { PAPERCLIP_WORKTREE_COLOR: branding.color } : {}),
   };