There is no default way to get a list of products that are eligible for the cart price rule because the cart price rule is applied at run time and catalogue price rule product collection works based on the predefine.
in simple terms, when the catalogue price indexer runs, it stores all
catalogue price rule eligible products in the database, and on the
frontend, it returns product collection from that table, and the cart
price rule is applied when users are on the cart page because there is
no data about eligible products in the database regarding the cart
price rule
So for achieve your requirement you have to do the customization.
There is 2 way.
Create your custom indexer class and store product ids in one custom table that is eligible for the cart price rule (recommended).
Create custom code to verify eligible product run time and return products accordingly (not recommended).
I hope this information will help you.
Thanks