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Among 4 pawns like white and black a&b pawns, you only need 1 pawn capture to allow the other 3 pawns to promote.

Great point.

So for each 4 pawn cluster, 1 pawn takes another pawn, and the net result is +1 bit once the captor promotes. The remaining 2 pawns in the cluster each need 2 extra bits when promoted => 2 x 2 = 4 bits. So 5 bits per 4-pawn cluster, of which there are 4.

So maximum representation would be 162 + (5 * 4) = 182 bits?

Yep, that increase the total in 3*3-4=5 bits, and you can repeat it 4 times, so the maximum is at least 162+4*5=182.

I'm trying to prove that is the worst case, but there are just too many cases. I guess I'll try to use a program o brute force it or just forget about it.

Actually, given this, we believe that 4 pawns must have been captured to reach 182 bits. So at least 4 pieces no longer need colors. If we store the color mask at the end, I think we can make it variable length, and truncate when no further pieces need colors assigned.

So then we need maximum 182 - 4 = 178 bits

EDIT: Equivalently, we could suffix each non-empty piece in the sequence with an associated color bit

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