Let's get this sorted out by performing some troubleshooting steps to get the Single time activity option show from the + New button.
One of the possible reason why isn't showing is that your browser stores frequently-accessed data, thus causing QuickBooks Online (QBO), to act weirdly. Let's try accessing your QBO account using a private browser to check if it's a browser data issue.
To start, log into your QuickBooks account using a private browser/incognito. Here's how:
Press Ctrl+ Shift + N keys on your keyboard (Google Chrome).
Press Ctrl+ Shift + P keys on your keyboard (Firefox or Internet Explorer).
Press Control+ Option + P keys on your keyboard (Safari).
If the private browsing session works, it means that you need to clear the browser's cache so the system can start fresh. You can also do this task on other supported, up-to-date browsers. Clearing the cache will refresh the system, and you'll be able to work with clean trash.
I'm adding these articles to learn more about entering a single timesheet in QBO: