This has been a source of confusion for me. I assumed that infinitives were verbs, but that isn't correct.
English grammar seems complicated.
I have tried to avoid splitting infinitives, but sometimes you step all over yourself in the process. In some cases, it is better to split the infinitive.
https://prowritingaid.com/split-infinitive
"Infinitives don't act as verbs. Rather, they act as
nouns, adjectives, or adverbs.
As nouns, they act as subjects of sentences or as direct objects:
To rescue Princess Aurora was Prince Philip's only goal. (subject)
A smart approach is to do a little each day. (direct object)
As adjectives, they modify nouns or pronouns:
His favorite toy to sleep with is his stuffed giraffe. (modifies toy)
As adverbs, infinitives modify verbs:
She ran to stay in shape. (modifies ran)"