I have not seen any Barnard specific numbers.
Barnard had, I believe, 9411 applicants last year.
Overall, applications seem to be up by about 10% (10% more common apps were submitted to colleges from roughly the same number of students). It makes sense that these would be concentrated among the more selective schools (including Barnard). A 35% increase in applications would be inline with reported increases at Tufts, Brown and Harvard.
That said, I will guess 12674 applicants this year.
Barnard College:
https://www.collegeconfidential.com/colleges/barnard-college/
Join Barnard Forum Discussions: https://talk.collegeconfidential.com/t/barnard-class-of-2025-decision-date-mar-31/2091526/1365