Dailyhalacha.com says as follows.
The Agudah says it is permitted as saliva not a food that is consumed. Others say it is not even considered food.
Chasam Sofer differentiates between the evening and the morning. At night, you should not swallow saliva, as the saliva still has the flavor of the food that one ate at the Seuda HaMafsekes. However by day, he says, you don’t have that problem, and you can swallow your saliva.
In summation, the Poskim all say clearly, that it is permissible to swallow the saliva on Yom Kippur.
Dailyhalcha.com concludes with the following quote.
Of course, one should not have Kavana (concentration) to collect the
saliva in his mouth and then swallow it in order to somehow quench his
thirst or something like that.