do 1600s overthink their moves
Are you sure 1300 players are actually playing better than 1600s, or they are winning because their opponents are also rated lower, or 1300 tactics don't work at 1600 level?
There are times where I lost because I do not calculate or think about the moves at all. At other times I either get too ambitious to try something or I overthink on a move when a simple move is readily available.
You said "Some ( and even many ) 1300 s play better then 1600 s"
You could be right about tactics, but I'm not sure whether they are better tactical moves, it could just be that those tactics are somewhat dubious but they work because also their lower rated opponent doesn't know how to handle them correctly. A sacrifice tactical combination at 1300 might rattle the opponent and work, but the same thing against a 1600-rated opponent may be punished.
Overthinking and taking longer to consider the moves might be slightly different too.
I don't believe a player can "overthink" a move. It's more a matter of drawing an incorrect conclusion from thinking about a move.
And there might be some cases where a 1600 is trying to force a certain plan, while the 1300 is playing more on a "move-by-move" basis. The 1600 might miss a certain a move because they're too focused on the bigger plan, while the 1300 might catch the blunder because they're only looking move-by-move.
Most of the time, though, the 1600 will see everything the 1300 does, and a bit more.