I agree here with Allan
In my personal opinion and not knowledge, I would think that the sliding keels were not coppered.
First of all it would be additional weight for lifting up.
Second the keels were relatively easily to be exchanged, if after years the would have some damages caused by woodworm
Third, the keels were solid wood, so no problematic if they would slightly rot..... no need of watertightness like on a hull
On the other hand, the rudders of ships were also coppered
But looking at the detailed drawings - there was so small space between the sliding keel and the shaft, that all copper sheathing of the keel would produce maybe some problem with the lifting - imagine, if one copper sheat would stand away, or one nail would be slightly too long etc....
View attachment 471903
View attachment 471904
These are drawings of the HMS Cynthia (1796)
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I think they had more problems to make the inside of the keel shaft watertight - maybe this part was coppered (but not visible in a model)
BTW: kenthistory is a very good page with often interesting and complete technical data of ships and the classes - worth to have a visit or two or three