For example, for a randomly generated password of 28 lowercase letters, which is about 128 bits of entropy, how would adding a space after every four characters affect it?
ijaxjnddkcswzovcrpbnqqiwaqyb ijax jndd kcsw zovc rpbn qqiw aqyb
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Adding characters to an existing password in such a fixed and known way does not alter its entropy as long as everything else remains the same.
In your specific case, adding a space every four characters can be seen as purely formatting to make passwords more readable.
Should an attacker not know about the formatting, the password just became six characters longer (and harder to brute force). If the attacker knows about the formatting they are back to brute forcing the password in a ~128 bit search space.
Small note: you could make the spacing a display property only (this might be doable with a web interface, difficult with a terminal).