As per my memory, DIGITS adds approximately 25MB of cloud storage for each DIGITS lines. It is shared among your contacts and messages. I believe messages are stored for approximately 4 days or so (from my practical experience). tmo_chris may provide more detailed info.
Hey, crownedmartyr! Thanks for asking. debjitjdv's recollection and practical experience here are honestly more detailed than the internal information we have available, which explains that messages are retained in the cloud for a few days to ensure that they're delivered to all of your devices, so I'll defer to him on this one. He has definitely logged the hours to be a reliable source!