You have to find where you are doing heterogeneous batch requests either directly or through libraries in your code. In any case batch requests are not reflected in your bucket logs because no API or API method per se was deprecated just a way to call send them.
In detail
You can bundle many requests to different APIs into one batch request. This batch will be sent to a one magical Google server that splits the batch and routes all the API requests in it into their respective service.
This Google server is going to be removed so everything has to be sent directly to the service.
What should you do?
I looks like you are making heterogeneous batch requests because only one service is mentioned, Storage. Probably you should do one of these options.
www.googleapis.com/batch
and replace it with the appropriate homogeneous batch API, which in your case is
www.googleapis.com/batch/storage/v1
- in case you use batchPath, this seems to be a relevant article
Otherwise, if you make heterogeneous calls with gapi, which doesn't seem to be your case, split something like this:
request1 = gapi.client.urlshortener(...)
request2 = gapi.client.storage.buckets.update(...)
request3 = gapi.client.storage.buckets.update(...)
heterogeneousBatchRequest = gapi.client.newBatch();
heterogeneousBatchRequest.add(request1);
heterogeneousBatchRequest.add(request2);
heterogeneousBatchRequest.add(request3);
into something like this
request1 = gapi.client.urlshortener(...)
urlshortnerbatch = gapi.client.newBatch();
urlshortnerbatch.add(request1);
request2 = gapi.client.storage.buckets.update(...)
request3 = gapi.client.storage.buckets.update(...)
storagebatch.add(request2);
storagebatch.add(request3);
Official Documentation
Here it's described how to make batch request specifically with Storage API.