Tough questions. If one walks into a room filled with Master Gardeners, it's likely there will be almost as many different answers as there are people in the room. (They're an opinionated bunch. ) There are so many variables to consider. I can share what I do and what has worked (or not) for me.
Soil is amended to improve the tilth. That is the suitability to support healthy plant growth.
Assuming we are talking about raised beds, and there is currently nothing growing in them, and depending on what I last planted, I may amend the soil with sterilized steer manure, Nature's Way composted mulch and some Dr. Earth fertilizer. If I have enough of my own homemade compost, I prefer that. Keep in mind that too much manure can increase the salts in the soil. If the bed last contained peas or beans (nitrogen-fixing legumes), then the nitrogen levels may just fine. Maybe the only amendments I add will be homemade compost. Remember we are discussing a living, dynamic ecosystem.
Examine a handful of soil--is it dark and rich? Does it have that "earthy smell"? You're probably good to go.
It doesn't surprise me that you still have some vegetables that are doing well. Some vegetable growth will span seasons. I have successfully nursed a cauliflower through the summer heat. Optimally, cool season vegetables taste best when grown in the cooler weather. Do you still have lettuce growing? When the temperatures rise, it becomes bitter. Snap peas actually do well and taste sweetest with a mild frost.
Generally speaking, it's difficult to successfully grow many vegetables during the hottest part of our summers. Having said that, I'll give some exceptions. Cantaloupe, watermelons, yardlong beans and blackeyed peas can be planted now. Okra and Armenian cucumbers thrive in the heat. If gardening with children, a sunflower or short-season pumpkins are a good choice. Just bear in mind the time to harvest.
Consider "square foot gardening". Instead of planting in rows, plant in a grid. That way a variety of vegetables can be planted. If you still have vegetables doing well in the heat and want to keep them, work amendments in the soil around them with a hand cultivator.
Experiment! If it is not enjoyable to garden in the heat of our summers, let the garden "rest" and plan what you and your family would like to grow and will eat during the cool season.