1. A system, comprising: a log-structured distributed storage system that maintains a log for a data volume, wherein updates to the log are assigned a log sequence number according to a log sequence number space for the data volume, wherein the log is segmented across a plurality of protection groups according to a partitioning of user data for the data volume such that a segment of the log and a partition of user data to which the segment of the log pertains are co-located together at a protection group, wherein each protection group comprises a plurality of storage nodes that provide redundant storage for a given segment of the log; and a storage client that processes access requests for the data volume and is configured to: in response to receiving an update to the log: determine a protection group of the plurality of protection groups according to which partition of user data space the update pertains; generate metadata to be included with a log record indicating the update, wherein the metadata comprises an indication of a previous log sequence number of a log record maintained at the protection group such that a position in a recovery sequence for the protection group and a position in the log sequence number space are identifiable; send the log record to the protection group; and based, at least in part, on acknowledgments received from one or more of the plurality of storage nodes implementing the protection group, identify the log record as eligible for durability in the log for the data volume.