in the various dry patches of the garden I sowed but does not grow grass
the fact that your turf presents spots, within which the grass does not grow even if it is re-seeded, suggests the possibility that some fungal disease has developed in these areas; if the dry spots are perfectly rounded, it could be a brown spot, caused by a fungus called rhyzoctonia, which also affects other plants, not just those of the turf; if instead the spots are sporadic, scattered here and there, it could be another fungal disease, whose pathogen is called pytium; to understand if this is really this type of fungal disease I invite you to check, comparing your lawn with the photos placed on this discussion of our forum
As laws in this exhaustive discussion, fungal diseases of the lawn are favored by fairly high night temperatures, associated with high humidity (due to damp air and rain, but also to excessive watering) and excessive nitrogen fertilization. To eradicate this type of fungal disease, it is necessary to use special fungicides to spray on the turf. It could also be problems due to the soil, which in those points is too hard and compact, and therefore does not allow the rooting of young seedlings of grass; in addition to the fungicide, it would be advisable to make a good aeration treatment of the lawn, so as to remove the felt that forms between the clods of grass, which often makes the soil almost impermeable; if necessary you will also have to intervene in the dry areas, hoeing the soil to make it softer, and enriching it with lawn compost; only then can you try to repeat the sowing.
I remind you that watering for lawns should not be administered excessively frequently, especially if the lawn is newly formed: little water supplied often, causes a very superficial development of the root system of the grass, and makes it easier prey of heat, cold, and water imbalances; proper watering is provided only when the soil is well dry, and must reach the areas even in depth, by interleaving the soil with water for at least 15-20 cm, so that in the days following watering, the grass roots are encouraged to grow downwards, in search of water. An always damp turf favors the development of many parasitic pathologies, which can ruin it also visibly.