This app was mentioned in 11 comments, with an average of 1.18 upvotes
If you have an android phone I'd recommend this app to help keep track of overtime. You can put in your hourly rate and a different rate for overtime if you get paid extra for it. Enter your shifts and edit start and leaving times if you do overtime and it'll show you the total hours you've done over the month and your pre-tax earnings.
The least bad, and closest to what you want that I've found is Shift Tracker doesn't connect to your calendar though, but has its own calendar view.
Shift tracker
https://play.google.com/store/apps/details?id=com.dgsd.android.ShiftTrackerFree
Just a note though in the pad the dev said he was going to stop work on it and released another similar app, then suddenly updated this app and pulled the new app. Which was annoying because I'd paid for the other one.
Can export of CSV I think on the paid version.
An alternative to that shift app is Shift Tracker
Shift tracker is the least bad that I've been able to find.
https://play.google.com/store/apps/details?id=com.dgsd.android.ShiftTrackerFree
I use this, it's the least bad app for tracking shifts that I've found.