Do General Aviation callsigns also have heavy or super when applicable?

I did not find anything in the forum revolving around this question discussing whether or not we use heavy or super when it is necessary for example when you’re flying a generic a330neo or a380. Can anyone quickly answer this one? It would really help me a lot since it sort of looks awkward when putting that in beside a general aviation callsign that is generally used for light aircraft…

“Heavy” is any plane with a maximum takeoff weight of 300,000 lbs or more, plus the Boeing 757. “Super” has no specific criteria, rather being assigned on a case-by-case basis, with the only two currently being the Airbus A380 and Antonov An-225.

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Thank you for the professional reply.

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