[lensoverlay] Update query submission time behaviour and add new param

1. Changed "qsubts" to be set at the url-generation time
representing when the url is created to be loaded in the side panel.
2. Added "pqsubts" to be set to when the user issued the query, i.e. the
old "qsubts" behaviour.

Bug: 422258998
Change-Id: Iabe24298fc4df859cbb7a020d0ac7e413e1b0ed2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6621458
Reviewed-by: Duncan Mercer <mercerd@google.com>
Commit-Queue: Jason Hu <hujasonx@google.com>
Cr-Commit-Position: refs/heads/main@{#1471347}