The field is saturated at the entry level, no question. It seems to be starting to lose a bit of luster, but there are still tons of bootcamp, micromaster, and MOOC graduates trying to break into the field every day.
Regarding the number of applicants, it depends. At the entry level it's a numbers game. There are tons of people who make well over 200 applications before they find their first job. The larger and more well known companies will attract tons of applicants. Smaller companies will still get several applicants, but nowhere near the number. There's also a big difference between the total number of applicants and the number of qualified applicants.
Anecdotally, we just opened up a Jr. Data Scientist role that had to be taken off the public facing site and moved to referral-based since we got close to 1000 applicants in 3 days.