[PixAL] Stop listening to app status after prompt is shown

The app needs to be observed only during the account linking flow to
trigger showing the prompt once.

To save resources, initialize the listener only during the account
linking flow, and reset after showing the prompt.

Bug: 425191286
Change-Id: I22ef637dbc5505948ccd9e9473a2cfd661cddf32
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6720622
Commit-Queue: Vishwas Uppoor <vishwasuppoor@google.com>
Reviewed-by: Rouslan Solomakhin <rouslan@chromium.org>
Reviewed-by: Siddharth Shah <siashah@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1487119}