Posting just because I looked all over and didn't see an answer. This function expands its arguments to canonical, absolute file paths, and tests whether one is a string prefix of the other. It also works for checking whether a directory is inside of or is identical to another directory.

local is_file_in_directory = function(file_path, directory_path)
  local file = vim.fn.fnamemodify(file_path, ':p')
  local dir = vim.fn.fnamemodify(directory_path, ':p')
  return file ~= nil and dir ~= nil and
      -- is dir an initial substring of file?
      file:find(dir, 1, true) == 1
end

This came up because I'm setting up obsidian.nvim which looks like a handy way to get the best of both worlds between Obsidian and Neovim. I'm setting up some custom configuration to automatically change the selected Obsidian workspace when I cd into vault directory, and to set conceallevel = 1 only on files in a vault, and that requires checking whether the working directory or a file path is inside a given vault directory.