* lisp/eshell/esh-proc.el (eshell-kill-process-function): Only reset
the prompt if PROC is writing to the terminal.
(eshell-sentinel): Only write the exit message if PROC is writing to
the terminal (bug#54136).
* test/lisp/eshell/esh-proc-tests.el (esh-proc-test/kill-pipeline)
(esh-proc-test/kill-pipeline-head)
(esh-proc-test/kill-background-process): New tests.