sunfish: Support switching session behavior types

This CL modifies `CaptureModeController` to allow switching between
behavior types when a capture mode session is already active, except
while in default capture mode session and the accelerator command to
start default capture mode session with a different source is pressed.

Demo: https://b.corp.google.com/issues/364720573#comment3

Test: added, verified it fails w/o fix in Patchset 1
Fixed: b/364720573
Change-Id: I2a4df6da84a99c780b692f4c3a70cb50bdf0e8f8
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5861671
Commit-Queue: Sophie Wen <sophiewen@chromium.org>
Reviewed-by: Ahmed Fakhry <afakhry@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1356825}