Certificate Management UI V2: don't re-use ClientCertStore objects

The normal ClientCertStore usage is that each object is used for a
single request. Since the UI can now refresh the client certs we
need to be able to get the cert list multiple times. Most of the
ClientCertStore implementations are actually fine with being used
multiple times but at least one that will be added in a followup CL
isn't, so just change to using them in the normal way.

Bug: 40928765
Change-Id: I45a42c71c52c1f511f9e7f7fb1d8cb03de24ce0b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5840362
Reviewed-by: Hubert Chao <hchao@chromium.org>
Commit-Queue: Matt Mueller <mattm@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1353390}