Yes it's possible, you could use Staging SP 2016 and then move directly to S2019.
You can reuse the SharePoint 2013 FBA database in SharePoint 2019. Configure FBA
I would prefer to setup the FBA 1st then migrates the Site collections from SP 2013 to SP 2019.
Setup FBA in SharePoint 2019 using existing DB.
if using the 2013 FBA database, backup the DB and restore in 2016 environment and then move it 2019, complete the SharePoint 2019 configuration (web.config changes, permission, STS configuration etc).
Below article for upgrading databases: https://learn.microsoft.com/en-us/sharepoint/upgrade-and-update/upgrade-service-applications-to-sharepoint-server-2019
Thanks & Regards,