69622 Move package:integration_test to flutter/flutter (cla: yes, team, tool)

69624 Say [APP] instead of [Gallery] in web benchmarks (cla: yes, team, waiting for tree to go green)

69629 Initial migration of metrics_center (cla: yes, severe: performance, team, team: infra)

69630 Update plugins dependencies for the Gallery test (a: null-safety, a: tests, cla: yes, team, tool)

69633 mark flaky tests as flaky (cla: yes, team, tool)

69693 Update dartdoc to 0.36.2 (cla: yes, team, waiting for tree to go green)

69696 mark flutter_gallery__transition_perf_e2e_ios32 flaky (cla: yes, team)