The backupformat does include .ikiwiki/aggregate so sites using aggregation, when restored, will think everything has been aggregated already, and will (probably, need to check) not re-create the aggregated files, which are not included.

Should the aggregate state file be included in the backup? If so, what about the source files aggregate stores, which are not in git by default, and so also not included in the backup?

done, not including aggregate in backup. Only downside really is that on restore a site won't have aggregated data for 5 minutes until the cron job triggers re-aggregation.