First, there are things that needs to be cleared up. The notable changes to v3 according to v3 Migration Guide are:
The differences between Drive API v3 and v2 are mainly changes to
field names and removal of duplicate functionality.
Notable changes
- Full resources are no longer returned by default. Use the fields query parameter to request specific fields to be returned. If left
unspecified only a subset of commonly used fields are returned.
- Duplicate and obsolete functionality has been removed. Examples:
- The Children and Parents collections have been removed. Use files.list instead.
- The Realtime.* methods have been removed. See the Realtime API documentation for alternatives.
- A number of field and parameter names have changed and affects accessing fields in resources as well as q and fields expressions.
Examples include:
- The property name is now used in placed of title.
- All date/time fields are now suffixed with Time instead of Date.
- Results from list operations no longer use a generic items field to contain the result set. Results are now included in a field named
for the corresponding resource type (e.g. files, changes, etc.).
- All update operations now use PATCH instead of PUT
- The exportLinks field has been removed from files. To export Google Documents, use the files.export method instead.
- The general approach for changes.list has changed. Opaque page tokens are now used in place of change ids. To poll the change
collection, first call changes.getStartPageToken for the initial
value. For subsequent queries, uses the newStartPageToken value
returned from changes.list.\
Notice that Google Sign was not mentioned contrary to what you've stated. I think it's just one of the alternative/easier ways to log-in. You can still use v2.
Check the v3 Android Quickstart for code reference if you ever want to use v3.