bug#71259: 29.1; Tramp connection property "direct-async-process" causes job control not to work in M-x shell buffers

[Alex Hutcheson via "Bug reports for GNU Emacs, the Swiss army knife of text editors" <bug-gnu-emacs@gnu.org>]

To reproduce:

1. Start emacs with emacs -Q

2. Eval the following:

(require 'tramp)
;; Enable direct-async-process for all SSH connections
(add-to-list 'tramp-connection-properties
              (list "/ssh:.*" "direct-async-process" t))

3. Start a Tramp SSH connection: C-x C-f /ssh:some.host.com:

4. Start a shell buffer with M-x shell. Choose sh or bash as remote
shell (haven't tested with others)

Expected behavior:

Shell buffer shows a shell on the remote host. Job control (C-c C-z),
fg, bg, etc. all work.

Actual behavior:

Shell buffer starts a shell, but shows errors at the top of the buffer:

sh: cannot set terminal process group (128765): Inappropriate ioctl for  
device
sh: no job control in this shell

Shell mostly works, but job control features don't work.
C-c C-z does nothing
C-c C-c kills the shell, rather than the currently running job
fg and bg give errors like:
sh: fg: no job control

In GNU Emacs 29.1 (build 1, x86_64-pc-linux-gnu, X toolkit, cairo
  version 1.18.0, Xaw3d scroll bars) of 2024-01-22, modified by Debian
  built on kokoro-ubuntu
System Description: Debian GNU/Linux rodete


Configured features:
ACL CAIRO DBUS FREETYPE GIF GLIB GMP GNUTLS GPM HARFBUZZ JPEG JSON LCMS2
LIBOTF LIBSELINUX LIBSYSTEMD LIBXML2 M17N_FLT MODULES NATIVE_COMP NOTIFY
INOTIFY PDUMPER PNG RSVG SECCOMP SOUND SQLITE3 THREADS TIFF
TOOLKIT_SCROLL_BARS TREE_SITTER WEBP X11 XAW3D XDBE XIM XINPUT2 XPM
LUCID ZLIB

Important settings:
   value of $LANG: en_US.UTF-8
   locale-coding-system: utf-8-unix