To see this in action, run "emacs -Q -f eshell" and then:

   ~ $ cd /sudo::
   /sudo:root@host:~ # *echo hi there > #<foo>
   Wrong type argument: "bufferp echo-stderr"

(Any other Tramp method should reproduce this issue.) That's because the 
echo command is being redirected to two places: stdout is going to the 
buffer "foo", and stderr is going to the Eshell buffer (via a pipe 
process). However, that doesn't work for Tramp processes.

Attached is a fix with a test. I think this should definitely go in 
Emacs 29, since it's a pretty bad regression. I'm actually surprised no 
one has filed a bug on this already.

For tracking purposes, I believe this was broken by f07505d1ec (bug#21605).

For Emacs 30, it'd be interesting to see if there were a way to get 
Tramp processes to have different targets for stdout and stderr. That'd 
make them work a lot more like local processes in Eshell.