I felt exactly this anxiety. In practice, most people pass probation fine — companies invest a lot to hire you and don't let people go casually. It felt precarious mainly because I was new and hyper-aware of everything.
My contract has a probation period where either side can end things with almost no notice, and coming from somewhere with strong protections it's making me anxious about signing a lease or committing to anything. Is this just normal and I'm overthinking it, or is it as precarious as it feels in the first few months?