We have a 4tb database with 64 tablespaces, 896 datafiles, putting this database in backup mode using alter tablespace begin backup commands would take 20 to 25 mins. Lately, it is taking over 2 hrs.
unheard of this problem.

is it for one tablespace or for all tablespaces?

Have you ever dropped tablespace and recreated?
Meaning, is there any "gap" in tablespace numbers?
You can easily check in v$tablespace.

Tamil