[tools/perf] Migrate profile_extender to new network controller API
[tools/perf] Migrate profile_extender to new network controller API

Migrate the profile_extender, used by the tools/perf/generate_profile
script, to use the new network controller API for Web Page Replay.

Depends on: https://codereview.chromium.org/1682813005/

BUG=404771

Review URL: https://codereview.chromium.org/1690603002

Cr-Commit-Position: 972c6d2dc6dd5efdad1377c0d224e03eb8f276f7@{#375162}

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