My climate is different from yours, and very variable. Some summers can be hot and dry (like this one was) but mostly it rains somewhat regularly, however, it is not uncommon that there's a short dry spell of a few weeks when nothing seems to germinate. I've struggled with germination, too. My current understanding is that there are two watering strategies that work: either a) do nothing at all and let nature handle it - the seeds will germinate eventually and hopefully in time to mature before the winter, or b) water them every single day when it doesn't rain, until they germinate, and water very thoroughly.
I've found that the worse thing I can do in my climate is to water them just a little bit every now and then. I think what happens then is that the seeds start germinating but then the tiny emerging seedlings die because there's not
enough water. Evaporation can dry the surface very quickly in sunny and windy conditions so shade clothing definitely helps in reducing the amount of water that is necessary to keep the bed moist until the seeds germinate.
Carrot seedlings are tiny and one little nip from slugs is all it takes to kill them. In my climate, if carrots do not germinate it is mostly because they did germinate but were eaten at night by slugs. This tip from the great no-dig
gardening guru, Charles Dowding, has finanally enabled me to grow carrots consistently, every year: Water well the rows where you're going to sow the seedlings, but just the rows, not the surrounding bed. Sow the seeds and cover them with DRY earth/
compost (about as much earth as the diameter of the seeds, not much that is, but do make sure it stays in place by tapping it down with your hand/ hoe / rake). Do not water again for two weeks at least. Carrot seeds are slow to germinate and being tiny, they do not need much water to germinate and grow. The extra water only invites slugs to the scene. Keep the bed weed-free and bare, no mulch, until the seedlings are big enough not to be easily eaten by slugs. Or if you must mulch, then use compost as mulch, but make sure it's not lumpy so it doesn't give the slugs a home.