Formal proofs may not be silver bullets, and we’re never safe from a faulty implementation of the proven algorithms, but this quanta article on a DARPA project showed impressive results [0].
There’s also AWS’ use of TLA+ [1].
[0]: https://www.quantamagazine.org/formal-verification-creates-h...
Many (most?) non-trivial bugs are actually flaws in the specification, misunderstandings about what exactly you wanted and what real-world consequences arise from what you specified.
You also aren't safe from misunderstanding what it is that you've proven about the program.
Which is actually the same problem as other software bugs; you have a specification of something, but you don't know what it is that you've specified, and you wish it were something other than what it is.
Interesting to think about a formal code verification system that maintained a connection between all four prime artifacts: natural language description of problem as understood & intended solution, vs. code and the properties actually verified.