There already is a post here explaining wether Shakespeare literally invented new words or simply put on paper words already existing orally but with his particular spelling that was kept in the english language as "standard" ever since.
Thing is, I am a native french speaker. So when I read about Shakespeare inventing words in english and come upon this, or this, all I can say is : Lol WTF ?
Why ? Because the overwhelming majority, if not nearly all of the words on theses lists literally are either french words with, or without, a slightly (but really slightly) modified spelling from french and pretty much exactly the same meaning than in french, that were (and still are for most) already in use both orally and written down for a really long time when Shakespeare was born; or latin words also with, or without a slightly modified spelling and that were used for a realllllly long time, way much longer than for the french ones, in latin; or french and latin words but with a more english suffix or prefix.
Maybe, maybe the small minority of words of germanic origin on theses list were indeed invented by Shakespeare, but for the rest, no, they weren't.
I mean, in french we use english words in everyday language too, but nobody pretend that some random french guy invented the words week-end, football, parking that we use, or that the french poet Charles Baudelaire invented the word spleen, obviously english, when writing Le Spleen de Paris.
Where does this belief that Shakespeare invented all theses words when he literally did not ? I mean, they are loanwords from french/latin not neologisms.
Shakespeare used 17,677 words in his writings, of which about one tenth had never (as far as we know) been used before.
This is a staggering display of ingenuity.
Some words Shakespeare gave us: barefaced; leapfrog; critical; monumental; castigate; majestic; obscene; frugal; radiance; dwindle; countless; submerged; excellent; fretful; gust; hint; hurry; lonely; summit; pedant;
These are some of the many words that are still with us. Some of Shakespeare's new words failed to catch on. We don't use "congreeing" or "congreeted". "Credent" did not generally catch on to mean "easily believed".
For new words to work, they have to have some logic or source so that the listener can understand and make sense of them. Shakespeare made new words in several ways:
He combined several existing words as in "Barefaced", "fretful", "countless", and "leapfrog".
He added meaning to an existing word as in taking "lone" and creating "lonely". (As per analogy with "happy" - "happily", "angry" - "angrily" etc.) with the interesting difference that "lone" is not usually used to express an emotion, but "lonely" does.
He took existing words and modified them to new purpose as in taking "majesty" and creating "majestic", or taking "critic" and creating "critical", modifying "radiant" to get "radiance", deriving "excellent" from "excellence".
"Radiant", of course comes directly from Medieval Latin, "radiantia".
"Dwindle" comes from the Middle English "dwinen" "to waste away or to fade".
Shakespeare used words that were at least somewhat familiar to his audience as the basis for many of the new words he coined. Thus he used many Latin, French and English words as the inspiration and basis for his linguistic creativity.
As you note, Shakespeare often took a Latin or French word and used it with a more English suffix or prefix. At the same time, this suffix or prefix often changed the nature of the word. Making a noun from a verb root or an adjective from a noun, for example.
Generally when Shakespeare outright uses a French or Latin word it is not counted as a new word, but when he uses a Latin word such as "radiant" to form the root of a newly coined word, "radiance" (which has a different meaning - though related), it is usually counted as a new word created by William Shakespeare.