Club option at $16.25M in the 9th season, then he becomes a FA when he is 31. So it is really more like a $146M contract (per Spotrac). Plus there is an additional $100M available through "escalators/incentives". Not sure of the details of that but on the radio they said one of them was winning rookie of the year (which is probably unlikely).
There is risk on both sides of this. The Sox are putting up a lot of money for a player who has 159 MLB at bats and only 2 HR. I am glad they did it, I think it is a good bet. For Anthony, he may be leaving money on the table but there is a lot that can go wrong between now and 2031 when he would otherwise become a FA. The absolute worst case is that he makes $146M 2026-2034. He will be 31 in 2034, so likely can get another big contract. I think overall, this is smart for him also.