As @ChristopherCounsell notes, what you are looking for is a group's capabilities. If you set the parameter users_update_items=True when you create a group, then 'updateitemcontrol' is added to the group's capabilities.
There are other capabilities a group can have, such as "distributed", so you should not rely solely on testing that capabilities is not null. I would recommend explicitly testing that 'updateitemcontrol' is in the group's list of capabilities.
You can specify a capability as part of your group search query, so one way to retrieve a list of shared update groups is:
shared_udpate_groups = gis.groups.search(
# A shared update group has 'updateitemcontrol' as one of its capabilites.
query = 'capabilities:updateitemcontrol',
# 10,000 appears to be a hard limit.
# If more than 10,000 might be returned, then split up your query and aggregate the results.
max_groups = 10000
)