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  3. Chess notation

Why is the move that White has to play in this position written as 29 Nec3 and not 29 Nc3. After all only one Knight can legally move to c3.

Regardless of whether there is only one night that can LEGALLY move to c3, it is simple notation convention that you always add the file the piece is in if you had two of the same pieces that could go to a certain square under normal circumstances.

Nc3 is sufficent and often used in situations like this.

It is probably just for technical reasons. Lichess doesnt check if a piece is pinned.

Some books do, some don't. Even the mighty Informator uses the explicit but superfluous notation in that cases.