It is difficult to tell much from the photos as they are too blurred.
Can't do better, I'm afraid.
Were those traces from your code? The data does not look to match what you have posted as your code.
The traces were from the I2CScanner code. As you can tell from the code, the program puts out many addresses. The scope is triggering on the SDA trace (blue), but it could be for any address.
Things to try:-
The code on the module's web site.
Did that some time back.
A different I2C library
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I'll try it.
It could be you have a faulty module.
I think that's the problem. When I first used the module, it worked fine. Then I put an 8 ohm speaker on the output. I read the manual later and it implies that the output should not be loaded at all - even the scope probe had to great an input capacity (some 100 pf). Since then its been misbehaving. But I didn't think the I2C system would be damaged.