Is there any protocol or functionality to analyze structural similarity between proteins? Thanks in advance
It's all contingent on what you mean by "structural similarity". In Rosetta we typically use either RMSD or GDT, and there's various ways of calculating that. One of the most straightforward way is to simply use the score application with the -in:file:native flag to specify the reference structure. Note that despite the name, it can take any structure as a reference.
One limitation of those approaches (in Rosetta, at least) is that they have to be for the same protein, or at least the same length of protein. If you want to calculate structural similarity between proteins of different lengths, you have to use a different program. I think DALI is a popular choice, but there's others. Those are structural alignment software, but most will also output some sort of "similarity" metric, if that's what you're after. Which metric they use depends on the package, though. (One of the MAMMOTH authors (Strauss) is a Rosetta PI, if that interests you at all.)