Replication reverted partitioned table to primary filegroup, can I re-link to the partitions?
Trying to be clever, we turned on replication to update the new server with the latest data on the large table, but that broke the partitioning and compression.

By default replication will initialize the subscriber with a copy of the table from the publisher.  This could have dropped your existing table on the subscriber.

On the physical disk, I can see the partition files, and they are still massive with GBs of data, so I know the data is there, but it appears the table has lost the link to it.

Replication won't change files or filegroups, but if the table on those filegroups was dropped, there's no way to recover it other than restoring a backup.
If you want to copy the publication data to the subscriber before starting replication, that's called Manual Initialization.  It allows you to tell replication that you've already initialized the subscriber and to just start applying changes.
Also when you set this up again, note that it's not normally necessary to land partitions on different filegroups.  It's more complicated and doesn't perform any better, so unless you are trying to put older data on slower disks, you can just put all the partitions on the same filegroup.  Using a non-default filegroup, and adding multiple (6 is a good choice) equal-sized files to the filegroup are both good practices.