Incorrect state of widgets on different tabs

[srirambv]

Description

Incorrect state of widgets on different tabs

Steps to Reproduce

1. Open a new tab and connect Binance widget
2. Open a second tab and follow steps from Widget looses connect state when network is disconnected #9253 to disconnect wallet
3. Go back to tab 1 from step 1 and try to select convert and check conversion preview
4. Go back to tab 2 and click on connect widget automatically goes back to the connected state

Actual result:

Incorrect state of widgets on different tabs

Expected result:

Widget state should remain same on all tabs

Reproduces how often:

Easy

Brave version (brave://version info)

Brave	1.9.21 Chromium: 81.0.4044.92 (Official Build) nightly (64-bit)
Revision	32921c79b6f01a0fb2deef0e1d45b42f96581051-refs/branch-heads/4044@{#883}
OS	Windows 10 OS Version 1909 (Build 18363.778)

Version/Channel Information:

• Can you reproduce this issue with the current release? NA
• Can you reproduce this issue with the beta channel? NA
• Can you reproduce this issue with the dev channel? NA
• Can you reproduce this issue with the nightly channel? Yes

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:

[srirambv]

Still reproduces on
Recording of the issue https://youtu.be/h33LRLgj_3E