feat(avbeat): point forum + auth at av schema, swap newsletter chips to AV verticals

Schema wiring — AV Beat was inheriting a 'bb' default schema from the
original fork. Fixed three call sites so the AV Beat app reads/writes
the av schema unless an explicit NEXT_PUBLIC_SUPABASE_SCHEMA override
is set:
  - src/lib/supabase/client.tsx:8 default 'bb' -> 'av'
  - src/lib/supabase/server.tsx:11 default 'bb' -> 'av'
  - src/app/api/auth/lookup-email/route.ts :31 + :42 hardcoded
    .schema('bb') -> .schema('av') so signup lookup hits the
    AV-side subscriber tables, not BB's.

Newsletter signup — homepage chips were the BB taxonomy ('Broadcast',
'Post Production', 'Animation', 'AI & Automation', 'Live Production',
'NAB Show'). Swapped for pro-AV verticals that align with the new
forum categories: Conference Rooms & UC, Digital Signage, Live Events
& Staging, Displays & LED, Audio, AV over IP, InfoComm & ISE.
Default selected flipped from 'Broadcast' to 'Conference Rooms & UC'
so the form doesn't pre-select a non-existent value.

src/app/api/auth/lookup-email/route.ts

@@ -28,7 +28,7 @@ export async function GET(req: NextRequest) {
 
   // Layer 1 — the rich subscriber registry (95k+ rows)
   const { data: sub } = await svc
-    .schema("bb")
+    .schema("av")
     .from("email_subscribers")
     .select("id, status")
     .eq("email_domain", email.split("@")[1])
@@ -39,7 +39,7 @@ export async function GET(req: NextRequest) {
 
   // Layer 2 — the lean property-specific list
   const { data: nl } = await svc
-    .schema("bb")
+    .schema("av")
     .from("newsletter_subscribers")
     .select("id")
     .ilike("email", email)