Improve Glic responsiveness recovery via immediate checks

Modify the Glic client responsiveness check logic to ensure only
one check runs at a time, waiting for a response before sending
the next.

Crucially, when a delayed response arrives (indicating potential
recovery from an unresponsive state), trigger the subsequent check
immediately instead of waiting for the standard interval. This
significantly speeds up the detection of restored responsiveness.

Also updated the test UI with a configurable duration input.
And corrected the unresponsive UI showing order typo.

Bug: 409776518
Change-Id: I8fc99b854c1aa6c904c44e0ec346df755266b94d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6452195
Reviewed-by: Dan Harrington <harringtond@chromium.org>
Commit-Queue: Aoyuan Zuo <zuoaoyuan@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1447323}