The maximum message limit for all folders combined (Inbox, Archive, and Trash) is 1,250. Once you reach this limit, you'll get a message telling you to delete some messages before you can receive new messages.
Note: If your device is below Android 6.0, the Inbox is limited to 150 messages, and the Archive folder limited to 500 messages.
Deleting messages from your Inbox moves them to the Trash folder, which does not reduce the 1,250 count. Best practice is to automatically delete messages from the Trash folder using the Preferences > Delete Messages option.