lobster: improve file naming

Risks of overriding files with existing name remain high. This CL uses
the `base::GetUniquePath` API to generate non-collidable paths.

Also move the logic to fetch file names and the logic to write file name
together to reduce TOCTOU issue.

Bug: b:359361699

Change-Id: Ic8bb53643189906f2173ac65687ef52d69a63077
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6261550
Reviewed-by: Curtis McMullan <curtismcmullan@chromium.org>
Commit-Queue: Chuong Ho <hdchuong@chromium.org>
Reviewed-by: Xiyuan Xia <xiyuan@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1420221}