nvim-tree not respecting diagnostics update_in_insert value set by neovim

Description

By default neovim sets diagnostics update_in_insert = false and other plugins (for example lualine) respects it. But somehow, nvim-tree doesn't.

Neovim version

NVIM v0.9.5
Build type: Release
LuaJIT 2.1.1710088188

Operating system and version

Debian 12 Stable (Linux 6.1.0-18-amd64)

Windows variant

No response

nvim-tree version

707b24a

Clean room replication

vim.g.loaded_netrw = 1
vim.g.loaded_netrwPlugin = 1

vim.cmd [[set runtimepath=$VIMRUNTIME]]
vim.cmd [[set packpath=/tmp/nvt-min/site]]
local package_root = "/tmp/nvt-min/site/pack"
local install_path = package_root .. "/packer/start/packer.nvim"
local function load_plugins()
  require("packer").startup {
    {
      "wbthomason/packer.nvim",
      "nvim-tree/nvim-tree.lua",
      "nvim-tree/nvim-web-devicons",
      -- ADD PLUGINS THAT ARE _NECESSARY_ FOR REPRODUCING THE ISSUE
    },
    config = {
      package_root = package_root,
      compile_path = install_path .. "/plugin/packer_compiled.lua",
      display = { non_interactive = true },
    },
  }
end
if vim.fn.isdirectory(install_path) == 0 then
  print "Installing nvim-tree and dependencies."
  vim.fn.system { "git", "clone", "--depth=1", "https://github.com/wbthomason/packer.nvim", install_path }
end
load_plugins()
require("packer").sync()
vim.cmd [[autocmd User PackerComplete ++once echo "Ready!" | lua setup()]]
vim.opt.termguicolors = true
vim.opt.cursorline = true

-- MODIFY NVIM-TREE SETTINGS THAT ARE _NECESSARY_ FOR REPRODUCING THE ISSUE
_G.setup = function()
  require("nvim-tree").setup {
    diagnostics = {
      enable = true,
    },
  }
end

-- UNCOMMENT this block for diagnostics issues, substituting pattern and cmd as appropriate.
-- Requires diagnostics.enable = true in setup.

vim.api.nvim_create_autocmd("FileType", {
  pattern = "lua",
  callback = function()
    vim.lsp.start { cmd = { "lua-language-server" } }
  end,
})

Steps to reproduce

1. Make sure lua-language-server is in $PATH.
2. Copy the above clean room replication into nvt-min.lua.
3. Launch neovim using nvim -nu nvt-min.lua.
4. Open nvim-tree using :NvimTreeToggle.
5. Open nvt-min.lua or any other lua file while keeping nvim-tree open.
6. Go to insert mode.
7. Create a diagnostic event (error, warning, etc.) by deleting some characters while in insert mode.
8. See that nvim-tree is updated (showing diagnostic icons) while in insert mode even though the default for neovim is update_in_insert = false.

Expected behavior

Nvim-tree respects the value of update_in_insert set by neovim.

Actual behavior

https://github.com/nvim-tree/nvim-tree.lua/assets/137637016/142b382d-c6b1-4669-9452-4575dcd780d4

As you can see, when I am creating an error in insert mode, lualine don't update the status but nvim-tree does.

I have checked the docs, issues and discussions and couldn't find anything related to it.

Start with the diagnostics configuration in require("nvim-tree").setup and reproduce the behavior using the supplied nvt-min.lua clean-room configuration. Compare nvim-tree's diagnostic updates with Neovim's update_in_insert setting while following the listed reproduction steps. Done means diagnostic icons do not update during insert mode when update_in_insert is false, while updates still work otherwise.