> Is this worse than trusting Twitter, Facebook, or TikTok?
Yes for the first two, no for the third. US-based companies are large targets for potential lawsuits, and consequently have processes in place to prevent random employees from accessing your DMs without cause. I obviously wouldn't trust those companies completely -- we're really arguing about probabilities here -- but there's at least some measure of accountability that makes them unlikely to do something trivially stupid.
> there are no private messages on Mastodon
It does have a DM feature -- that they aren't private is exactly the point.