[Code Health] Remove a use of base::SupportsWeakPtr. (ppapi)

Bug: 40485134
Change-Id: I8f0a24a364ca6f6cb81c072f297af6ca55018794
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5639216
Commit-Queue: Dave Tapuska <dtapuska@chromium.org>
Reviewed-by: Derek Schuff <dschuff@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1317027}
NOKEYCHECK=True
GitOrigin-RevId: 0b0bee3828bc68a05a87e268368d9562c70cda49
2 files changed