If several apps that were open before restart come back, deselect Reopen windows when logging back in in the restart or logout dialog. If the same app opens at every login, check System Settings → General → Login Items & Extensions and remove it from the list of items that open at login.
01If the last session comes back after a restart
Section linkSave your work and choose Restart or Log Out from the Apple menu. In the confirmation dialog, clear Reopen windows when logging back in. If macOS skips that dialog, it uses your most recent setting. Test at the next sign-in by checking whether apps from the previous session reappear.
02If one app opens at every login
Section linkOpen Login Items & Extensions and select the app in the list of items that open at login. Click the minus button to remove it. The app stays installed. If the app keeps opening and is missing from the list, check its own preferences for a launch-at-login option. Leave background permissions alone if you only want to stop an app window from opening.
03If old windows return when you open an app yourself
Section linkOn macOS Ventura or later, open System Settings → Desktop & Dock and turn on Close windows when quitting an application. On earlier macOS versions, look in System Preferences → General. For a one-time test, hold Shift while opening the app to skip its saved windows.