These operations fall under cleaning and repairing meshes inside Meshlab… To quote its function from docs, please check following image from Meshlab documentation
These should be easy to produce with the infrastructure in Meshes.jl. For example, given a mesh you can extract the graph of vertices as an adjacencymatrix(mesh), use Graphs.jl to find the connected components and then use the vertices(mesh) to decide whether or not a component satisfies a given criterion for removal. Of course there are many details to address, but the building blocks are there.
Feel free to reach out in our Zulip channel if you have more specific questions or if you would like to implement these functions yourself.