Alter UpdatePrintSettings API to use context ID

After https://crrev.com/1117252, UpdatePrintSettings() is no longer
called as a regular query for Print Preview.  It is now only used prior
to invoking the system print dialog or at the start of printing a
document from Print Preview.  This significantly changes the use case
for it, as now it can always require a context ID when it is used
out-of-process.

This change in API requires an OOP printing context to be established
earlier.  It also affects StartPrinting() since the settings are now
only longer needed at this time when the system print dialog is invoked
from in the browser.

This facilitates some cleanup, since the Mojo PrintTargetType is no
longer necessary.  It is now sufficient just to know if the print job
is from a system dialog.

Bug: 1414968
Change-Id: Ib5e50263df54b550216525dbd10a83e6ee3efff4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4256086
Reviewed-by: Lei Zhang <thestig@chromium.org>
Commit-Queue: Alan Screen <awscreen@chromium.org>
Reviewed-by: Nasko Oskov <nasko@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1121921}

• chrome/browser/printing/print_backend_browsertest.cc[diff]
• chrome/browser/printing/print_backend_service_manager.cc[diff]
• chrome/browser/printing/print_backend_service_manager.h[diff]
• chrome/browser/printing/print_backend_service_test_impl.cc[diff]
• chrome/browser/printing/print_backend_service_test_impl.h[diff]
• chrome/browser/printing/print_job_worker_oop.cc[diff]
• chrome/browser/printing/print_job_worker_oop.h[diff]
• chrome/browser/printing/print_view_manager_base.cc[diff]
• chrome/browser/printing/printer_query_oop.cc[diff]
• chrome/browser/printing/printer_query_oop.h[diff]
• chrome/browser/printing/system_access_process_print_browsertest.cc[diff]
• chrome/services/printing/print_backend_service_impl.cc[diff]
• chrome/services/printing/print_backend_service_impl.h[diff]
• chrome/services/printing/public/mojom/print_backend_service.mojom[diff]
• printing/printing_context.cc[diff]