Move database package source code under pkg

[sitole]

Move all database package files under the pkg module to make it cleaner and Go-compliant.
Requested at #1365

---

Note

Relocates the database module to packages/db/pkg and updates imports, sqlc outputs, Dockerfiles, and env handling in the DB client across the codebase.

• DB package:
  • Move sources to packages/db/pkg (e.g., pkg/client, pkg/queries, pkg/types); update sqlc.yaml outputs to pkg/queries and type overrides to pkg/types.
  • Change pkg/client.NewClient to read POSTGRES_CONNECTION_STRING via os.Getenv and error if unset.
  • Update packages/db/Dockerfile to build migrator from cmd/migrator; adjust paths; slim builder.
  • Update packages/db/Makefile generate target to pkg/queries.
  • Refresh packages/db/go.mod deps; add/remove indirects.
• API and services:
  • Update all imports from db/{client,queries,types,dberrors} to db/pkg/{client,queries,types,dberrors} across handlers, orchestrator, template-manager, utils, cache, edge pool, and team modules.
  • Adjust packages/api/Dockerfile to copy ./db/pkg instead of individual subdirs.
• Seeds/Tests/Shared:
  • Update seed scripts and integration tests to new db/pkg/* imports.
  • Add replace github.com/e2b-dev/infra/packages/db => ../db in packages/shared/go.mod.
• Generated code:
  • Regenerate sqlc files under packages/db/pkg/queries with updated package paths.

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[sitole]

Make tidy now complains about cycle dependency (shared - db - shared). Not sure why it was not an issue before.

[sitole]

Make tidy now complains about cycle dependency (shared - db - shared). Not sure why it was not an issue before.

The build fails because the shared dependency is now on the db package, and we need to add it to all Dockerfiles, even if the database is not used there. I don't like it, and we should move the seed database script out of shared, so it's not needed.