the first question is if you've confirmed that bsa/bdssa 8.9 both support sqlserver 2016.  did you confirm that first ?

if 8.9 supports the version of the database you want to upgrade to, then i don't think it matters what order you do the change over.  as long as the database is up and reachable at the end of whatever migration you do and you have updated any changed configurations in bsa/bdssa then it should work.