ReadyCallback should be a repeating callback (uplift to 1.11.x)

[brave-builds]

Uplift of #5847
fix brave/brave-browser#10271

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• You have checked CI and the builds, lint, and tests all pass or are not related to your PR.
• You have tested your change on Nightly.
• The PR milestones match the branch they are landing to.

After you merge:

• The associated issue milestone is set to the smallest version that the changes is landed on.

[kjozwiak]

Looks like test-browser failed on Linux as per https://ci.brave.com/job/pr-brave-browser-pr5847_issues-10271_1.11.x/1/execution/node/417/log/.

15:40:58  1 test crashed:
15:40:58      BraveRewardsBrowserTest.AutoContributionMultiplePublishersUphold (../../brave/components/brave_rewards/browser/rewards_service_browsertest.cc:1855)

However, seems like an intermittent issue and not related to this specific PR.

test-install also failed on macOS as per https://ci.brave.com/job/pr-brave-browser-pr5847_issues-10271_1.11.x/1/execution/node/646/log/. However, this is a known issue and doesn't block uplift as it's not related to this particular PR.

[kjozwiak]

Uplift into 1.11.x approved after deliberating with @brave/uplift-approvers. QA has also verified the PR on Nightly as per #5847 (comment).