I'm looking for fiction books in which an entity with a soul attempts a singularity with the human race, the latter without a soul.

You might be best off going to a large library with a good English language fiction collection and browsing their collections or asking a reader’s advisory librarian. Your asks are often too specific in nature for us to answer.

What is a “soul?” You’d best define the term if you’re going to use it.

Damon Knight wrote a short SF story about a party of explorers who are absorbed by alien protoplasm. Their bodies are digested but their brains and neural tissue are preserved so they remain conscious with their memories intact. It isn’t at all as gruesome as you might expect. The short story was called “Four in One” but it may not be what you had in mind.

Maybe something relating to the John McCain Presidential campaign.

There are aspects of the book Contact (not in the movie) that might help.