The mushrooms do not directly affect the plants, but they are a symptom of a problem.

First though... what "got dry and died"? The mushrooms, or the zucchini? And, are these plants in the ground?

One of the problems is over-watering. Mushrooms only grow in moist conditions. While containers of different forms are a separate case, the best way to think of watering plants in the ground is 1" of water per week. Up to 2" or so during hot weather. This includes rain. Also, there's an axiom that will serve you and your plants well... water deeply, but infrequently.

So, starting early in the season, you want to water the ground heavily enough that the soil is moist to a deeper point than the roots reach. Then you want to let the top few inches of soil dry out. This will encourage the roots to grow downward, 'searching' for moisture. When the plants are young, and the roots are only a few
inches long, you'll want to water more often - spreading that 1" out so
that the soil around the roots doesn't dry too much. But as the plants
mature, he surface needs to dry. This has the added benefit of discouraging molds and fungi which prefer moist conditions.

If you water too often, and the roots always have access to water at the surface, they don't have to grow deep. The deeper you can get the roots to grow, the more 'reserves' they will have during the hottest days of summer. The deeper underground - the cooler the soil. The plants will be less affected by heat if the roots are in deep, cool, soil.

Also. a mulch will help both cool the soil and preserve it's moisture. A good mulch will help lessen the need for frequent watering.

Thank you very much, Rgreen48! You answer was very clarifying! It's amazing to see how nature works in such logical way as you've explained.

About your question I was afraid that the zucchini plants got dry and died, and maybe that's why I have exaggerated on the watering frequency. I now noticed the fungus disappeared, the soil is less humid, but the base of the plants seem to be weaker (picture). I'm concerned... Could I do anything to help them recover?

Thank you so much again!!

It's tough to see on that image, but you may have other problems causing the base of the plant to be 'weaker'.

Over-watering definitely stresses the plants and sets up incubation conditions for both pests and disease. To stick with the watering issue, and while you may be able to help this plant along for this year, I'd consider this a learning experience. Most of the root growth and formation of the plant is established early during the vegetative growth stage. Once fruiting has begun on plants like zucchini it's tough, and usually not worth, trying to get it to go back into a growth phase. It will continue to grow, but for annuals like squash, fruiting is a priority.

Since your plant is somewhat established, you can begin the new watering regimen, but keep an eye on it. If the roots are too shallow, you may have to cater to it's water needs a bit. You can though, put down a mulch. I recommend an organic mulch. A 2" layer of compost is an example, and things like hay or straw work well with squash and have the benefit of keeping the fruit up off the ground, protecting them from molds and rotting.

The mulch will help the ground retain moisture, so that even shallow-rooted plants can do a bit better during summer's heat. Get your fingers down into the soil. Generally, with well established plants, you want the top 2" - 4" to dry out before you water. Watch the leaves, if they look a little wilted then it may need watering.

Squash is susceptible to a number of pests that can attack the stems and weaken the plants. The squash vine borer is the most destructive, but squash bugs, and cucumber beetles will also cause the plant to weaken. If you see the leaves wilt, but watering doesn't help, you'll know that there's a pest or disease issue.

Then there's molds and mildews. They too cause a plant to weaken quite a bit. Unfortunately, all these problems can eventually kill the plant. White, 'powdery' stuff on the leaves is a common problem, as well as yellowing of the leaf margins and 'blotches'.

Presenting all these issues may seem like it's more problems than it's worth, but when you get the hang of it, squash is a good crop to grow. Especially zucchini, once given a good start, will outgrow, and produce buckets, faster than anything can kill it lol.

I'm not sure this will help with this year's plants, but next year.... Oh, if you grew from seed, depending on where you live, you might be able to
sow a few seeds now and have a fall harvest. Zucchini's are fast
growers, and while they are susceptible to a number of problems, once
you get the watering worked out, planting in 'succession' can be a quite successful.