Android
Mark All Messages as Read auf Android
Google Messages marks conversations as read individually to avoid accidentally hiding a text you have not actually opened yet. The bulk action sits behind the account menu because it affects every conversation at once, not just the one you are currently viewing.
To clear all unread threads, open Messages and tap your Google Account icon in the top corner. Select Mark all as read from the menu that appears.
This removes the unread badge from every conversation immediately. Google Messages does not ask for confirmation, so check that you actually want to dismiss all unread texts before tapping the option.
The action cannot be undone. If you only want to catch up on one or two conversations, open them individually instead of using the bulk option, since there is no way to restore the unread status afterward.
The icon for the account menu can look slightly different depending on your device, but the Mark all as read entry stays in the same place.