Keep in mind the great majority of Shakespeare's contributions to the language are not neologisms in the strict sense. Most repurpose existing vocabulary in a new and useful but straightforward way. A noun becomes a verb. A noun is given a productive and familiar adjectival suffix. A back-formation invents a noun (which the hearer is happy to assume existed all along) from a familiar verb, etc. If I were to say a fruit has a "lemony" sourness, or a "melony" sweetness to it, my audience would not be confused, regardless of whether these words are familiar to them. The very productive "-y" adjectival suffix is well enough known that any such "inventions" are immediately understood.

Shakespeare's vocabulary is never inaccessible on a Joycean level. And where it is inaccessible, it means to be so, for specific contextual reasons. Shakespeare does not mean "Honorificabilitudinitatibus" to be a comprehensible word. He means it to be preposterous, extravagantly inaccessible Euphuism.

The Elizabethan dramatic corpus has something of an unfair advantage, when it comes to perceived word production, given that it is (if frequently in a mannered fashion) documenting spoken language, the vocabulary of which might well have existed in oral use for some time prior without finding a place in the written corpus, particularly given the relative poverty of surviving 15th and early 16th century literary and especially dramatic production in English.

When people say Shakespeare "invented" these words, they mean that he was our first source for them. We can assume that he was using words in his widely popular plays that people up and down the class system would understand.

Two examples:

Shakespeare is given as the source of the word eyeball. Both the words eye and ball already existed, he is just the first recorded source to put them together.

Shakespeare has the first use of the word assassinate. Assassin was a preexisting noun, Shakespeare just turned it into a verb.