The main advice with two way data syncing is to ensure that you've mapped out the data flows and make sure that it's clear which system needs to be updated to update data. I once worked on a PHP monolith that worked with a vendor .net system where because the data flows were incorrect, would routinely overwrite data changes, especially for fixed/updated changes. We eventually did a large project which fixed the data flows and cut the number of complaints to 20-30% of the original volume.
How you set up these syncs really depends on the ingest/egress options for the systems in question. Are you pulling data directly from a db? Do you need apis? Etc