Is this what you’re looking for? I’ve demonstrated 2 ways to do it.
The first is with the button triggering a modifyRows() formula.
First you tell it what row you want to modify. The row you want to modify is “something from Table A” (which row?) “filter to just a row that is the same data as Column 1 of the row I’m pushing the button from”
Then you tell it what column to modify (“status”)
Then you tell it the value it should be (yes/no)
The second is simpler formula-wise. It puts the buttons on the first table, and then brings them into table B as related columns to the lookup column.