Improve rewards onboarding experience (uplift to 1.18.x)

[brave-builds]

Uplift of #7135
Resolves brave/brave-browser#12675
Resolves brave/brave-browser#12612

Approved, please ensure that before merging:

• 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]

Restarting Win x64 via https://ci.brave.com/job/pr-brave-browser-pr7135_ksmith-rewards-onboarding-fixes_1.18.x-windows/ as it appears as CI failed Check out from version control as per https://ci.brave.com/job/pr-brave-browser-pr7135_ksmith-rewards-onboarding-fixes_1.18.x-windows/3/execution/node/85/log/.

[kjozwiak]

test-browser failed on Win x64 due to https://ci.brave.com/job/pr-brave-browser-pr7135_ksmith-rewards-onboarding-fixes_1.18.x-windows/7/execution/node/246/log/. However, the reward timeout is an intermittent issue and doesn't block uplift.

12:20:00  1 test timed out:
12:20:00      RewardsBrowserTest.BackupRestoreModalHasNotice (../../brave/components/brave_rewards/browser/test/rewards_browsertest.cc:303)

[kjozwiak]

Uplift into 1.18.x approved after deliberating with @brave/uplift-approvers. QA has verified the PR on Nightly as per #7135 (comment).