Looking at the words שבת שבתון (ex. Vayikra 23:24) and שבתות (ex. Vayikra 23:15) and there root שבת what do endings ון- and ות- indicate here? What do these suffixes mean/indicate?
P.s. Are there any other examples of words build up this way?
Regarding שבתון, see Ramba"n on the verse that you alluded to in your question. It's long, but the essence of his explanation is near the beginning. He says this means that it is a day of rest. From reading the rest of the commentary, it seems that indirectly, he may be explaining the difference between שבתון and שבת . (BTW, I just noticed in your Q you mentioned both words together. That's not in this verse, but later on regarding Yom Kippur.)
While both words do imply a day of rest, שבת is generally used to refer either to the 7th day of the week, or sometimes it means just "week". So, perhaps, to avoid confusion, the Torah uses the word שבתון to clarify that one should rest on this day even though some form of melacha is permissible on Yom Tov, unlike on שבת .
The word שבתות in 23:15 means, simply "weeks". There was a "debate" among the Pharisees that argued that in this verse it means "Shabbat", i.e., the 7th day of the week. Thus, they took this to mean that Shavuot always occurs on a "Sunday".