It would be definitely be simpler to have Google Assistants that trigger 4 separate flows, each with a distinct url in the maker Thing.
But you can do it the way you are attempting, but with some changes.
First, you would need to use the 'variable value' parameters, not the variable names. But just changing that in your flow still won't work, you will only get one variable value.
Think of each connection line as carrying a signal to the next action Thing, along with any parameters. You press the first button, which triggers two Variable things to set your two variables. Both of those connect to the Maker Thing. But their signals cannot arrive simultaneously. Whichever gets there first will pass its parameter to the Maker, and activate the Maker to run. It won't wait for the other parameter. A Stringify tech called that a 'race condition'.
You need to have both parameters passed from one variable Thing.
Have your your triggers set the variables, like you are doing now, but without any connections coming off of the right of them.
Above or below your Variable Things, put a timer. Initially set it to 5 seconds. Draw connections from every trigger, so that in addition to setting the variables, they will all start the timer.
At the end of the timer, put another variable Thing, configured to 'get the value of variables', and put in your two variables. Have that connect to the Maker, and use the variable value parameters. That way there will be only one signal from one variable Thing going to the Maker, but it will pass both variables.
About that timer...
When you change a variable in Stringify, you need to allow some time for the change to take affect. That can take less than a second, but sometimes longer. I guess it depends on how busy Stringify is at the time. If you don't wait long enough, your flow will get the wrong value when it reads or uses the variable. But longer times can be annoying if you are waiting for a result. So start with a 5 second timer, then once you get it working, you can try shorter times. Too short and your flow will intermittently fail.