What you do yourself in the app is never notified, and a project with Show notifications unticked never notifies.
Every notice is a Windows notification, also when the SyncNow window is in front, and the same when it is behind another window, minimized or hidden in the notification area: nothing appears inside SyncNow. There is one per project: the post itself, for example www.example.com · Conversations with who wrote and the conversation's subject, or 5 new updates in www.example.com when several arrive together, with a line for each of the first three (more than three projects at once are summed up in one). Clicking it brings SyncNow back on that post in its tab (the conversation, the plan, the rule or the Activity entry), on the project for several posts of one project, or on Projects for several projects.
The notifications carry SyncNow's name and icon and stay in the Windows notification center until you sign out, also after SyncNow is closed: since version 13.2.49.79 clicking one then starts SyncNow and, once you are signed in, opens what it is about (Projects if that project is not on this PC); with SyncNow already open the click goes to the open window. Signing out removes them. If none appears, open Windows Settings > System > Notifications: Notifications must be on, and SyncNow on in the list of apps; Do not disturb holds them back. SyncNow checks every 30 seconds while you are signed in, across all your projects, and right after you sign in. On the PC SyncNow keeps only the time of its last check for your account, never subjects or projects; the first check on a PC looks back 15 minutes, and after a long pause at most 7 days. See How do follow-up questions and clarifications work?.