Re:
The fact its only happening when you put stress through the pedals suggests something is worn and the new chain isn't meshing correctly.
I assume everything was indexed & working OK before the new chain, but as things have now been swapped in/out it could be hard to say for certain.
New chain, new cassette, new chainring, then you can be sure you've ruled those 3 out.
I've had chains slip on worn chainrings before and been sure it was the cassette as the rings looked "OK" to me, it's also hard to see if it's slipping at the front or rear when riding. And I also hoped a new chain would stretch and in time fit the older csssette/, rings.... It didn't.
If you get it working nicely then you can try swapping in the M770 cassette, see if the problem returns, then you'll know if it was that or the rings.
Also check the chain for stiff links.
If that doesn't sort it then it's time to get a new bike