How to tag people in discussion board in SharePoint online?
Also will they get notified if they are tagged?
how to get the the site feed ??
Discussion Board does not support @mentions or #hashtag. Hence you cannot tag people in discussion. Alternatively you can use Site Feed or News Feed. Both are for different purpose but if designed correctly it can be alternative to discussion board.
Refer below blog for difference between them and how both works. https://sharepointmaven.com/newsfeed-or-discussion-board/
Site Feed webpart screenshot, please make sure you have created classic page. it is yet not available in modern page.