Activity tab doesn't auto-update the status of transactions

[srirambv]

Description

Activity tab doesn't auto-update the status of transactions

Steps to Reproduce

1. Submit a transaction
2. Switch to activity tab
3. Shows unapproved state of transaction
4. Open panel and approve the transaction or reject the transaction
5. Activity tab continues to show the unapproved transaction state
6. Doesn't remove the transaction on its own have to reload if rejected
7. Doesn't change to Submitted/Confirmed/Error unless there is a page reload

Actual result:

Activty.Tab.mp4

Expected result:

Should update the transaction state without user refreshing the activity tab page

Reproduces how often:

Easy

Brave version (brave://version info)

Brave	1.52.102 Chromium: 113.0.5672.126 (Official Build) beta (64-bit)
Revision	c541687b21a73452ab403e2dced7033ddc97ee9d-refs/branch-heads/5672@{#1202}
OS	Windows 11 Version 22H2 (Build 22621.1702)

Version/Channel Information:

• Can you reproduce this issue with the current release? NA
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Not checked

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? NA
• Does the issue resolve itself when disabling Brave Rewards? NA
• Is the issue reproducible on the latest version of Chrome? NA

Miscellaneous Information:

cc: @Douglashdaniel @josheleonard @onyb

[srirambv]

Verified as part of #28800 (comment)