window.ethereum is not available after reloading page for default wallet setting changes

[spylogsster]

Description

if users have opened tabs that work with window.ethereum object and enable native Brave Wallet using another tab then the object will not be available after reloading tabs. it becomes available only after opening a new instance of tabs.

Steps to Reproduce

1. Set Wallet type preference to None
2. Open chainlist.org in a new tab
3. Set Wallet type preference to Brave Wallet
4. Go to tab with chainlist.org and reload it
5. check window.ethereum object in console

Actual result:

the object is not available

Expected result:

the object available and work as expected

Reproduces how often:

100%

Brave version (brave://version info)

Version/Channel Information:

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

Other Additional Information:

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

Miscellaneous Information:

[srirambv]

Brave	1.36.100 Chromium: 98.0.4758.102 (Official Build) beta (64-bit)
Revision	273bf7ac8c909cde36982d27f66f3c70846a3718-refs/branch-heads/4758@{#1151}
OS	☑️ Linux	☑️ Windows 11 Version Dev (Build 22523.1000)	☑️ macOS Version 12.0.1 (Build 21C52)
	Verified steps from brave/brave-core#12193 Verified when default provider is set to None, window.ethereum returns undefined Verified after changing default provider from None to Brave Wallet, window.ethereum returns a response when the same page is reloaded
	20993-Linux.mp4	20993-Windows.mov	20993-macOS.mov