It's kinda complex.

I think my initial stab would be to encoding the source position (6 bits) and end position (6 bits) for a constant 12 bits per move.

You don't need to store whether it's a capture, you can figure that out from the game state. You don't need to store disambiguations, there are none in that format. You don't need to store check/mate, you can figure that out from the game state.

The only wrinkles (that I can tell) are castles and promotions. But you can get around this by the fact that kings and pawns have limited movement, so their legal destination squares are highly constrained.

So you could signal a promotion by encoding the destination with opposite rank, and using the file to encode which piece. Promoting to a rook on c8 gets its destination encoded as a1 - "a" for a rook, and "1" to indicate a promotion.

Similarly, you could encode a castle by encoding the king's move with opposite destination rank. Castling the king to f1 gets encoded as f8, and to g1 as g8.