How to properly replicate and archive at once
Let me explain multiple things.  Then you can figure out which combination fits best.

Technically the Primary and the Replica should have identical data.  However...
You can, via a temporary setting, say that specific statements are not to be replicated.  These could be anything -- INSERT, Partition commands, DROPs, etc.
It sounds like you want the data to be moved from fast media to slow media.  This would require some form of copy.  And that would probably block all operations (maybe even SELECTs) from the table while it is happening.
It may be possible to direct that certain PARTITIONs are in a different filesystem path.  If so, that secondary path could be the other drive.
&quot;Transportable tablespaces&quot; allows for an individual PARTITION to be disconnected from a table and turned into an independent table.  That could them be copied to another device, backed up, deleted, etc.  (Do not do it via filesystem operations.)
It is probably wise to switch to PARTITION BY RANGE(TO_DAYS(...)) with daily partitions.  This would facilitate such movement and eventually deleting after 60 days.
PARTITIONing applies to a table, so there is no need for doing it with all tables.  (Perhaps you are referring to &quot;sharding&quot;, which involves having separate, independent, instances of MySQL with each one having part of the data.
If you have not already set up partitioning or replication, there will be a one-time cost (in downtime) to set up either.  After that, ongoing maintenance will be 'cheap'.
More on this use of partitioning:  http://mysql.rjweb.org/doc.php/partitionmaint