I like your last question in that sentence. Some other answers could be....
Vaccines are overall a net positive so it's better to hide the negative affects.
The opioid situation was so obvious there was simply no way to keep it hidden.
More powerful people would go down with the vaccine scandal.
I'm not saying any of those are true. Just giving some possibilities reasons to your very reasonable question.
To your conspiratorial leanings, I will say this...
It never surprises me when rich and powerful people do some dirt to get more rich and powerful. So, at some point, if a story came out that some pharm corp applied some pressure somewhere they shouldn't have, or tried to cover something up, I would not be shocked. But vaccines, and drugs in general, are tested with great rigor. And they are tested independent of the pharm corps that produce them. So, we don't hear stories like that often because it is difficult/impossible for pharm companies to pull off such a swindle.
The opioid scandal had nothing to do with the effectiveness of oxycontin, or of immediate side effects. It had to do with ignoring reality (the "slow release" formulation meant to minimize the high and hence addictiveness was meaningless because patients were crushing and snorting), and highly unethical distribution practices (https://pmc.ncbi.nlm.nih.gov/articles/PMC2622774/).
If you want to wage war on the pharm giants, I think they have it coming in many cases. But mostly for price inflation and unethical marketing, not hiding evidence that their drugs are a sham or dangerous. But even in that sense, these companies are largely playing within the rules, so we get back to our broken, profit-driven healthcare system.