I understand you are having a problem with Outlook for iOS showing “connection to the server failed” and you can still access the mailbox on your laptop. Please confirm which account type is this (Outlook.com/Hotmail, Gmail/Yahoo, Microsoft 365 work/school, or on‑prem Exchange), and does the same error happen on both Wi‑Fi and cellular?
I would love to hear from you soon. Have a nice day!