During any heatwave, people with heart and blood pressure issues suffer extra. Usually heat waves result in extra deaths especially among elderly people or obese people. High temperatures combined with high humidity are particularly dangerous even before they get lethal for healthy people.
Increasing frequency and severity of heat waves are definitely a noticeable thing. My parents actually lived in the South of France for a few years after their retirement. They were there in the last few weeks for a brief vacation and temperatures went well over 40 degrees in June. That used to be unusual even in the hottest month (July) and is now a yearly recurring thing. Luckily, humidity tends to be quite low in that particular area. But still, 40-45 degrees is a lot to deal with for people.
I think migration will be more an indirect consequence of local economies collapsing when e.g. agriculture becomes hard/impossible due to rising temperatures. People tend to move for economic reasons. Any mass casualties in a wet bulb heat event might of course cause people to panic. But richer countries would be able to compensate with technology by e.g. desalinating water and having buildings with AC. It's poor countries that lack the means for this that are going to suffer most.
Neal Stephenson has some nice perspective on this in his latest novel Termination Shock where people in e.g. Texas are dealing with temperatures that are basically not survivable without a so-called earth suit, which is a battery powered cooling solution people wear to be able to be outside in 50 degree+ Celsius heat. Those might become an actual thing people would need to own pretty soon in some places.