Could it be that I drowned my seedlings?
Do you mean that you planted seeds or set out seedlings? If you planted seeds -- what kind were they? Some plants might take that long to germinate. If the drainage is good, they probably didn't drown. Maybe the weather is too cool for them to sprout. Really need more info to be of much help.
If you are talking seeds, Kale should be up in 5-10 days, tomatoes 7-14, cukes 7-10, squash 7-14, so you should be seeing something by now. Peppers usually take at least 2 weeks, but last year and this year, my peppers are taking longer.
20 degrees Celsius is about 68 F. My tomatoes and kale do ok at that temperature, but cukes, squash and especially peppers do better with more heat.
I agree with Don, you should definitely be seeing something by now. Peppers are all over the place and can take anywhere from 5-6 days up to several months. The rest, you should have something by now. My tomatoes, zucchini, squash, cucumbers, watermelon, eggplant, etc. usually pop within about 4-10 days and I often just germinate them at room temperature. Peppers I keep around 85F.
What are you using to germinate them? What kind of potting mix did you use? How deep did you plant them? As long as the potting mix drains well then they should be fine with the water. I germinate in a domed mini greenhouse seed starter and spray the top of the potting mix regularly to keep it moist. You want to keep the seeds from drying out and keep the humidity high when germinating, so moisture normally shouldn't be a problem unless you're using poorly draining potting mix.