VPN connect / reconnecting may not have a proper timeout

[bsclifton]

Description

Reported by @stephendonner. He had connected to VPN and then turned off WiFi. Clicking VPN button, it looks like it's trying to reconnect - but there's no timeout. It should timeout and transition to the error state

This may have the same root cause as #22754

Steps to Reproduce

1. Enable VPN (see test plan in Implement Brave VPN on Desktop #15804 for more information)
2. Click VPN button (next to hamburger menu) and connect to a server
3. Disconnect your network (if plugged in with ethernet unplug, if on WiFi disable)
4. Click VPN button again - it should be trying to reconnect

Actual result:

It gets stuck saying "Connecting..."

Expected result:

It should error out and show the error page in VPN panel

[spylogsster]

This may have the same root cause as #23028

[stephendonner]

Verified PASSED using

Brave	1.41.36 Chromium: 102.0.5005.78 (Official Build) nightly (x86_64)
Revision	df6dbb5a9fd82af3f567198af2eb5fb4876ef99c-refs/branch-heads/5005_59@{#3}
OS	macOS Version 12.5 (Build 21G5027d)

Followed the test plan from brave/brave-core#13504 (comment).

Steps:

1. enabled VPN (see test plan in Implement Brave VPN on Desktop #15804 for more information)
2. clicked VPN button (next to hamburger menu) and connected to USA (West), which is my geo-detected default
3. disabled Wi-Fi
4. clicked VPN button again - it should quickly try to reconnect, then...
5. confirmed VPN dialog's status is accurate, and now says Disconnected
6. confirmed toggling VPN when Connected/Disconnected keeps accurate connection state(s)

Initial disconnect is much slower then subsequent ones - I'll have to chase that up separately 👍

[MadhaviSeelam]

@spylogsster
I am confused as to expected result for this issue on Win 11x64. I see error modal Can't connect server in Win 11 x64.
Expected result mentioned in the issue says show error page and test plan in the PR says show disconnection status. @stephendonner tested this in 1.41.36 nightly and got correct status as per the test plan. It's failing for me in the 1.41.36 nightly as well. I am not sure if this behavior is restricted to macOS

[MadhaviSeelam]

This issue VPN connect / reconnect is not working as expected. @stephendonner filed a follow up issue #23924 as above.
@spylogsster @rebron @bsclifton