[BUG] Session names don't sync between Claude macOS app and Android app (both directions)

Summary

Renaming a Claude Code session on one device doesn't propagate to the same
session viewed on the other device. Sync is broken in both directions —
desktop→mobile AND mobile→desktop.

Repro

1. On the Claude macOS app, hit Remote Control on an active session and name it

"Report Claude mobile image-upload bug"

1. Open the same session on the Android app
2. Mobile shows the session as the literal string "1." (not picked up

from the desktop-set name)

1. Rename it on mobile to "bug reporting"
2. Switch back to the macOS app — desktop still shows the original

"Report Claude mobile image-upload bug" name; the mobile rename did
not propagate either

Expected

Session name set on either device propagates to the other within a few
seconds. Whichever device renamed last wins.

Actual

Each device retains its own local name. Neither rename reaches the other
device. The mobile-side default name appears to be a literal placeholder
("1.") rather than picking up the desktop-set name at all.

Environment

• Desktop: Claude macOS app
• Mobile: Claude Android app 1.260423.20, Pixel 10 XL, Android 16
• Date observed: 2026-04-30