[BUG]: Renaming the current file using :Rename (from vim-eunuch) doesn't update the winbar

[Flimm]

Requirements

• [X] I have skimmed other issues to see if this bug has already been reported.
• [X] I'm fully certain that this is not a breaking change, see the latest release.
• [X] This plugin and its dependencies are up to date with the latest commit.
• [ ] I'm willing to fix this through a PR.

Expected Behavior

I am using :Rename from vim-eunuch. When I run :Rename newname.txt, I expect the winbar to be updated to show the new filename newname.txt.

Actual Behavior

Instead, the old filename remains displayed in the winbar, although the new filename is displayed in the bottom status bar.

Neovim Version

NVIM v0.10.0
Build type: Release
LuaJIT 2.1.1713484068
Run "nvim -V1 -v" for more info

Minimal Configuration

local root = vim.fn.fnamemodify("./.repro", ":p")

-- set stdpaths to use .repro
for _, name in ipairs({ "config", "data", "state", "cache" }) do
  vim.env[("XDG_%s_HOME"):format(name:upper())] = root .. "/" .. name
end

-- bootstrap lazy
local lazypath = root .. "/plugins/lazy.nvim"
if not vim.loop.fs_stat(lazypath) then
  vim.fn.system({
    "git",
    "clone",
    "--filter=blob:none",
    "--single-branch",
    "https://github.com/folke/lazy.nvim.git",
    lazypath,
  })
end
vim.opt.runtimepath:prepend(lazypath)

-- install plugins
local plugins = {
  -- do not remove the colorscheme!
  "folke/tokyonight.nvim",

  {
    "utilyre/barbecue.nvim",
    dependencies = {
      "neovim/nvim-lspconfig",
      "SmiteshP/nvim-navic",
      "nvim-tree/nvim-web-devicons",
    },
    config = function()
      require("barbecue").setup()
    end,
  },
  { "tpope/vim-eunuch" },
}
require("lazy").setup(plugins, {
  root = root .. "/plugins",
})

-- add anything else here
vim.opt.termguicolors = true
-- do not remove the colorscheme!
vim.cmd([[colorscheme tokyonight]])

Reproduction

1. nvim -u repro.lua
2. :w oldfilename.txt
3. :Rename newfilename.txt
4. The top winbar displays oldfilename.txt even though it should display newfilename.txt. (The status bar displays the expected new filename, though)