Rewards button pre-opt-in badge dismisses after first button press (uplift to 0.72.x)

[brave-builds]

Uplift of #3898
Fixes brave/brave-browser#6691

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 macOS due to the following failure as per https://ci.brave.com/job/brave-browser-build-pr/job/pr3898_rewards-stub-dismiss-badge_0.72.x/1/execution/node/665/log/:

17:17:08  [37461/38641] CXX obj/v8/torque_generated_initializers/array-foreach-tq-csa.o
17:17:28  Cannot contact mac-imac2-ky: java.lang.InterruptedException
18:06:00  Could not connect to mac-imac2-ky to send interrupt signal to process

Restarting Win x64 due to the following failure as per https://ci.brave.com/job/brave-browser-build-pr/job/pr3898_rewards-stub-dismiss-badge_0.72.x/1/execution/node/241/log/:

14:27:45  Cannot contact i-07fb2dbe053cc5fcf: hudson.remoting.RequestAbortedException: java.io.IOException: Unexpected termination of the channel
14:32:49  Could not connect to i-07fb2dbe053cc5fcf to send interrupt signal to process

[kjozwiak]

Restarting on Win x64 due to https://ci.brave.com/job/brave-browser-build-pr/job/pr3898_rewards-stub-dismiss-badge_0.72.x/2/execution/node/541/log/ failing.

[kjozwiak]

Uplift into 0.72.x approved after deliberating with @brave/uplift-approvers. This fix was also uplifted into 0.71.x as per #3914 and will need to be uplifted into the remaining channels. Both CI/Jenkins and CI/Travis passed after several restarts.