feat(backend): add install_id to PostHog events

Include SOURCEBOT_INSTALL_ID in PostHog event properties for better
tracking and analytics. Also removes unused import in web posthogProvider.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: brendan-kellam

packages/backend/src/posthog.ts

@@ -24,6 +24,7 @@ export function captureEvent<E extends PosthogEvent>(event: E, properties: Posth
         properties: {
             ...properties,
             sourcebot_version: SOURCEBOT_VERSION,
+            install_id: env.SOURCEBOT_INSTALL_ID,
         },
     });
 }

packages/web/src/app/posthogProvider.tsx

@@ -4,7 +4,6 @@ import { usePostHog } from 'posthog-js/react'
 import { PostHogProvider as PHProvider } from 'posthog-js/react'
 import { usePathname, useSearchParams } from "next/navigation"
 import { Suspense, useEffect } from "react"
-import { env } from '@sourcebot/shared/client'
 import { useSession } from 'next-auth/react'
 import { captureEvent } from '@/hooks/useCaptureEvent'