Another thousands of people have died after the vaccine 
Well, actually it's probably true that thousands of people have died after the vaccine, but not because of the vaccine. A lot of people are getting vaccinated, many of them old, and everyone dies eventually. So saying there were thousands of post-vaccine deaths is true, but probably misleading.
-About 675 million people globally have had at least one vaccine dose
-In a normal year pre-COVID, if you took 675 million people representative of global demographics, about 4.4 million of them would die, so averaging 365,000 per month
-Vaccinated people probably skew older and sicker, so you would actually expect more than 365,000 deaths per month, globally, among people who have been vaccinated, even if the vaccine did nothing good or bad.
So since mass vaccination has been going on for a few months now, unless at least >1 million people globally have died some time after being vaccinated, you'd start to think that these vaccines might be a sort of miracle drug that not only protects you from COVID, but also prevents you from dying from anything else 
That is almost certainly not the case. But it also means that even if someone can point to data showing thousands of deaths in vaccinated people, that does not in and of itself even remotely suggest that the vaccines are dangerous.