nordvpnlite fix wait for start

[tomasz-grz]

Problem

There is a race condition between TelioContext::new() and handle_exit_node_connection():

1. handle_exit_node_connection() starts making API calls.
2. TelioContext::new() calls set_ip() -> /etc/init.d/network reload and disrupts the network stack.
3. Current in flight API calls can fail.

Solution

1. Move handle_exit_node_connection() to run after TelioContext::new() completes.
2. Broaden retry logic (exponential backoff for all API calls).
3. Add additional DNS logs to restart test.

☑️ Definition of Done checklist

• Commit history is clean (requirements)
• README.md is updated
• Functionality is covered by unit or integration tests

[djkarwowski]

I've left just one comment, but overall looks good to me

+1

[mathiaspeters]

+1

[lcruz99]

this looks a nice improvement, however would be nice to add some logs or ticket ID to the PR, besides the usual commit history cleaning before merge :)