[lensoverlay] Hold contextual queries until server response

The server needs more time to process the PDF, so sending the request
immediately after the upload is finished allows the contextual query
to be process before the page content. This CL changes the contextual
query to be held until the server has responded to the page content
upload which guarantees the server has started processing the page
content prior to the contextual query.

Fixed: 395103461
Bug: 393368667
Change-Id: I815cef57525b209eaa3e20b4ce356dfe8eb515e7
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6242787
Commit-Queue: Duncan Mercer <mercerd@google.com>
Reviewed-by: Bryan Nguyen <nguyenbryan@google.com>
Cr-Commit-Position: refs/heads/main@{#1417613}