Why every 30 minutes, and not every block?
Apple asks apps to receive no more than two or three background pushes an hour. A ping on every block would exceed that budget. Mainnet blocks are about 75 seconds today and about 25 seconds after the NU7 upgrade, so each wake covers on the order of 72 new blocks on a phone.
Shielded alerts versus watching a transparent address
Many block explorers and node APIs can push activity on transparent addresses. Shielded Zcash payments do not appear on a public address list. Lantern Zero's scanning mode trial-decrypts compact blocks and the mempool with a viewing key you lend for a short lease, then sends an encrypted push and a hint list of heights to scan first. That is a wallet notification path, not a merchant checkout webhook.
Why this is not a light wallet server
Your wallet still downloads compact blocks from the light wallet server it already uses. Lantern Zero only tells it when to sync and, in scanning mode, which blocks to prioritize. It does not replace lightwalletd or Zaino.
Why this is not a merchant webhook
Checkout tools watch a shop's receiving key and POST to a server when a customer pays. Lantern Zero connects to a user's wallet through a connection URL and wakes the app on the phone. Shops need a till and invoice flow; that is a different product track.
What the server can see
In default mode the server learns that your account exists and which devices to wake. It never holds a viewing key. Every client request uses Oblivious HTTP through a relay run by a third party, so the relay sees your IP but not the request body and the server sees the request but not your IP. In scanning mode the operator can see incoming payments to the lent key while the lease is active; the key stays only in memory and is never written to disk, logs, or backups.
Read the FAQ, integrate as a wallet developer, see what Tachyon changes, or read the protocol spec on GitHub.