## Problem
If a repository is added **after** a search context (e.g., a new repository is synced from the code host), then it will never be added to the context even if it should be included. The workaround is to restart the instance.
## Solution
This PR adds a call to re-sync all search contexts whenever a connection is successfully synced. This PR adds the `@sourcebot/shared` package that contains `syncSearchContexts.ts` (previously in web) and it's dependencies (namely the entitlements system).
## Why another package?
Because the `syncSearchContexts` call is now called from:
1. `initialize.ts` in **web** - handles syncing search contexts on startup and whenever the config is modified in watch mode. This is the same as before.
2. `connectionManager.ts` in **backend** - syncs the search contexts whenever a connection is successfully synced.
## Follow-up devex work
Two things:
1. We have several very thin shared packages (i.e., `crypto`, `error`, and `logger`) that we can probably fold into this "general" shared package. `schemas` and `db` _feels_ like they should remain separate (mostly because they are "code-gen" packages).
2. When running `yarn dev`, any changes made to the shared package will only get picked if you `ctrl+c` and restart the instance. Would be nice if we have watch mode work across package dependencies in the monorepo.
