I am sure that if the FEDERAL minimum wage is increased to $ 15, some states have already done so, it will make some things go up - but the increase isn't all at one time; it's staggered - When it begins to hit the prices of daily living, it will increase the cost of living and will be added into the SS benefit as a Cost of Living Adjustment (COLA).
Before any adjustment in overall benefits, other than some COLA when they happen, the balance sheet of the Social Security Trust Fund has to be shored up. Let's hope Congress can get together on this problem sometimes in the next few years; there are lots of different plans -
Thus far, President Biden has only signed an EO to increase the minimum wage on those FEDERAL employees and those employed under Federal contractors who make less. I doubt there are a lot of these, especially enough to affect the bottom line cost of most Americans. Before the minimum wage is changed for the Nation as a whole to a minimum of $ 15 per hour, Congress has to do it by law - the President can only support this effort - Congress has to do the actual acting.