Use a recognisable test
Send a chat and an email with unique subjects and no real customer details. Confirm both arrive in Tickets and that the channel and sender context are correct.
Work like an agent
Claim or assign each test, send a reply, change its status, and check the response at the original browser or email account. Ask a second teammate to confirm that ownership updates for them too.
Finish the launch check
Close the test tickets and confirm they leave the active view. If one channel fails, use its troubleshooting guide before advertising the desk to customers.