〜と links to a following verb (or other predicate)
〜との links to a following noun (or noun equivalent)
That's generally what の does—indicates a relationship to a following noun:
海へ 行く The particle へ links 海 to the following verb 行く
海への道 The particle の links 海へ to the following noun 道
In English, we use word order instead of a particle:
go [ to the sea ]
the road [ to the sea ]
We can tell that the to-phrase relates to the verb go or to the noun road because they're next to each other. But that doesn't work in Japanese—you need to specify that it relates to a noun by adding の.
Likewise, in your example, 好きなアニメと needs の to relate to the following noun, コラボ. In English we could just say "collaboration [ with 〜 ]", but in Japanese you need to add の.