GreXXL thanks. I also found another workaround: I click on the "All Discussions" dropdown in the upper part, then in the list I click again on (the already selected) "All Discussions" item and it effectively reloads the home page.
P.S. BTW, I think Pusher doesn't work in PWA mode which is probably the main reason why there is a need for a refresh button. I guess it may be an iOS limitation. Also, the free Pusher plan will allow only 100 simultaneous connections and if it worked in PWA mode that would mean that suddenly there will be as many connections as there are PWA users (unless the websocket is closed when the app is not in focus).
