Update UI on component update (uplift to 1.10.x)

[brave-builds]

Uplift of #5724

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]

Looks like test-browser failed on both Linux & macOS due to BraveRewardsBrowserTest.CheckIfReconcileWasResetEmpty as per the following:

• Linux - https://ci.brave.com/job/pr-brave-browser-pr5724_SR_components_update_dp_1.10.x/1/execution/node/407/log/
• macOS -https://ci.brave.com/job/pr-brave-browser-pr5724_SR_components_update_dp_1.10.x/1/execution/node/530/log/

4:33:02  Failed
14:33:02  RunLoop::Run() timed out.
14:33:02  Stack trace:
14:33:02  #0 0x55d8d4e50769 (/home/ubuntu/jenkins/workspace/pr-brave-browser-pr5724_SR_components_update_dp_1.10.x/src/out/Release/brave_browser_tests+0x5c3c768)
14:33:02  
14:33:02  [  FAILED  ] BraveRewardsBrowserTest.CheckIfReconcileWasResetEmpty, where TypeParam =  and GetParam() =  (30859 ms)

However, the above failure isn't an uplift blocker as brave/brave-browser#10032 was fixed in Nightly.

[kjozwiak]

Uplift into 1.10.x approved after deliberating with @brave/uplift-approvers. QA won't be able to run through the PR on Nightly but after discussions with @deeppandya and @srirambv, we'll merge this and QA it when we get 1.10.x release builds.