Here's what I do. Any search key will turn hlsearch on and will turn it off.

vim.on_key(function(char)
  if vim.fn.mode() == "n" then
    local new_hlsearch = vim.tbl_contains({ "<CR>", "n", "N", "*", "#", "?", "/" }, vim.fn.keytrans(char))
    local esc = vim.tbl_contains({ "<Esc>" }, vim.fn.keytrans(char))

    if new_hlsearch then
      vim.opt.hlsearch = true
    elseif esc then
      vim.opt.hlsearch = false
    end
  end
end, vim.api.nvim_create_namespace("auto_hlsearch"))