This study has multiple issues as did the original study it is accompanying but what got published in Nature Medicine
https://www.nature.com/articles/s41591-021-01630-0First the original study did not stratify based on age and sex - a huge failure because potential issue among young men was well known problem.
This preprint tries to fix this but as the original study compared also other cardiac adverse events like pericarditis and cardiac arrhythmias, the preprint does not. It is important because the rate of other complications was not elevated among vaccinated.
This study uses self-controlled case series. This means that they compare against previous incidence rates in the study group (vaccinated, covid-19). This would be possibly more or less fine if they compared two treatments but even then there is big potential for selection bias (the choice of treatment is based on preexisting conditions) but is even higher when you compare treatment and disease - covid-19 is harder for people with comorbidities, when you make a comparison within this group, you can most likely expect higher preexisting prevalence of heart conditions and therefor lower IRR.
This preprint and the orginal paper do not contain any mentioning of unvaccinated. It very likely means that the covid-19 group also contains patients who were vaccinated and had lower rate of AE.
Finally, this study design includes people with previous incidence. Hearth problems are very often recurrent. While it is important to know if vaccination of covid-19 will reintroduce the condition, it is not very interesting for most of the people because incidence rate of these conditions is very low. What is real interest here is how prevalent it is among people who did not have it previously.
Now I am really interested to find out the truth here. This preprint and the orginal study does not help me in this unfortunately.