This concern must be taken in context, myocarditis is also a side effect of COVID-19 infection.
https://www.sciencedirect.com/science/article/pii/S266633762...
Last year a Red Sox pitcher missed an entire season due to myocarditis caused by COVID-19 infection.
https://www.espn.com/mlb/story/_/id/30929594/red-sox-p-eduar...
I computed that on the day when I got my vaccine (the first dose was AZ) and the risk of thrombosis from the vaccine was comparable to that of that of thrombosis from corona in the next few weeks, assuming that my risk of being infected was the average for the city and that the incidence would be stable over the next weeks.
Three weeks I think? So the vaccine raised my chance of thrombosis in the next two weeks by 50%, but cut my chance of thrombosis in the next six weeks by 50%. Pick a number according to the conclusion you'd like to see.
Not necessarily long-term. I would suggest that short-term effects such as thrombosis of myocarditis, however rare, are also a valid cause for concern.