Using New Outlook on Windows for personal email, calendar, and contact management
Hello,
New Outlook does support this, but the option is hidden.
Left-click the red-underlined word, then select the three dots (…) in the correction pop-up and choose Add to dictionary. Do not only hover over or right-click the word.
Microsoft’s instructions are here: https://support.microsoft.com/en-us/word/add-or-edit-words-in-a-spell-check-dictionary
If Add to dictionary is still missing, update New Outlook from Microsoft Store > Library > Get updates, restart it, and test again at https://outlook.live.com/.
If it is missing in both places, the feature is not working correctly for your current account/build. Editing RoamingCustom.dic is not a reliable fix. Please report it through Help > Feedback in New Outlook. Until it is corrected, the reliable alternative is classic Outlook, which provides right-click > Add to Dictionary.