NEXRAD weather radars are commonly used, but also things like portable vertical-looking radar systems
It’s not just limited to swarms – even individual migrating birds can be detected. See birdcast, which produces live maps of birds flying over areas in the US (https://birdcast.info/). Other taxa include things like mayfly swarms (see this paper: https://www.pnas.org/doi/abs/10.1073/pnas.1913598117). You can detect flying insects of all kinds in the air during the summer, although distinguishing them seems not yet possible. This is an area with a lot of active ongoing research, but has already been shown to be a valuable monitoring tool for many groups. There is a lot of literature on the topic to dive into if you’re interested in learning more.
I think this is still a little contentious. People have been claiming that we are seeing bird migration on weather (rain) radars for a while and while it seems quite plausible - these noisy patterns typically occur in migration periods - I am not sure if it’s generally acceptable. Recently people even started claiming migrating butterflies and other insects.
There are weather radars (to detect rain) in most developed countries around the world. They usually have local websites for display, so you have to look at this country by country. The Windy app for example shows data from all around the world in one place but I am not sure if this kind of events are well visible there as they tend to filter the data against “artifacts”.
Not contentions at all. This brief paper gives a pretty solid overview, including some interesting things, like being able to track wingbeat frequency.