Surprised nobody has mentioned this
https://www.gevenalle.com/product/audax/ but these are what you probably want. You are not going to find a 2X5 integrated brake/shifter and 2x7 is of no real quality these days and you would want to find a 7 speed cassette which would require a new wheel and doing a lot more work that is a pain. However the Gevenalle gives you the reliability of those downtube friction shifters with the convenience of the all in one package with I think better shifting. With STI and similar levers you cannot really sweep your freewheel or cassette as one might do with down tube or bar end shifters but you don't have to take your hands off the brakes to shift with Gevenalle you can do both.