* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/sigpipe-exits-process): Use "|&" when creating the
pipeline to prevent an extra pipe process from being started.

* lisp/eshell/esh-proc.el (eshell-put-process-properties): Pass INDEX.
(eshell-gather-process-output): Create a pipe process for stderr when
stderr goes somewhere different than stdout.
(eshell-insertion-filter, eshell-sentinel): Consult
':eshell-handle-index' property.

* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/output/stdout-to-buffer)
(esh-proc-test/output/stderr-to-buffer)
(esh-proc-test/exit-status/with-stderr-pipe): New tests (bug#21605).

This allows tracking this information for process objects not recorded
in 'eshell-process-list', which will be useful for pipe processes for
stderr output.

* lisp/eshell/esh-proc.el (eshell-process-list): Add docstring.
(eshell-record-process-object): Only record the process object and
whether it's a subjob.
(eshell-remove-process-entry): Adapt to changes in
'eshell-record-process-object'.
(eshell-record-process-properties): New function...
(eshell-gather-process-output): ... call it.
(eshell-insertion-filter, eshell-sentinel): Use new process
properties, don't require process to be in 'eshell-process-list'.

* test/lisp/eshell/esh-proc-tests.el (esh-proc-test--output-cmd): New
variable.
(esh-proc-test--detect-pty-cmd): Add docstring.
(esh-proc-test/output/to-screen)
(esh-proc-test/output/stdout-and-stderr-to-buffer)
(esh-proc-test/exit-status/success, esh-proc-test/exit-status/failure)
(esh-proc-test/kill-process/foreground-only): New tests.
(esh-proc-test/kill-background-process): Rename to...
(esh-proc-test/kill-process/background-prompt): ... this, and use
'eshell-wait-for-subprocess' instead of 'sit-for'.

* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/pipeline-connection-type/middle)
(esh-proc-test/pipeline-connection-type/last): Set 'debug-on-error' to
nil.

Ref: https://lists.gnu.org/archive/html/emacs-devel/2022-08/msg01452.html

* lisp/eshell/esh-cmd.el (eshell-exec-lisp): Handle
'eshell-pipe-broken'.

* lisp/eshell/esh-io.el (eshell-output-object-to-target): Only signal
'eshell-pipe-broken' if the process being written to has finished.

* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/pipeline-connection-type/middle)
(esh-proc-test/pipeline-connection-type/last): Remove ':unstable'.

Ref: https://lists.gnu.org/archive/html/emacs-devel/2022-08/msg00524.html

* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/pipeline-connection-type/middle): Mark test as unstable
as it fails quite a lot.

* test/lisp/eshell/esh-proc-tests.el
(esh-proc-test/pipeline-connection-type/last): Mark test as
unstable as it fails quite a lot.

* test/lisp/eshell/eshell-tests-helpers.el
(eshell-command-result--equal, eshell-command-result--equal-explainer)
(eshell-command-result-equal): New functions.

* test/lisp/eshell/em-basic-tests.el
* test/lisp/eshell/em-dirs-tests.el
* test/lisp/eshell/esh-cmd-tests.el
* test/lisp/eshell/esh-proc-tests.el
* test/lisp/eshell/esh-var-tests.el
* test/lisp/eshell/eshell-tests.el: Use 'eshell-command-result-equal'.

This was formerly named 'eshell-command-result-p', but "result" isn't
quite the right terminology, since this function specifically tested
the output of a command, not its Lisp result (as
'eshell-command-result' would return).

* test/lisp/eshell/eshell-tests-helpers.el (eshell-insert-command):
Provide a more-complete docstring.
(eshell-match-result): Rename to...
(eshell-match-output): ... this.
(eshell-match-output--explainer): New function.
(eshell-command-result-p): Rename to...
(eshell-match-command-output): ... this.

* test/lisp/eshell/em-alias-tests.el
* test/lisp/eshell/em-dirs-tests.el
* test/lisp/eshell/em-extpipe-tests.el
* test/lisp/eshell/em-script-tests.el
* test/lisp/eshell/esh-cmd-tests.el
* test/lisp/eshell/esh-proc-tests.el
* test/lisp/eshell/esh-var-tests.el
* test/lisp/eshell/eshell-tests-helpers.el
* test/lisp/eshell/eshell-tests.el: Use 'eshell-match-command-output'.

* src/lisp.h (emacs_spawn):
* src/callproc.c (emacs_spawn): Add PTY_IN and PTY_OUT arguments to
specify which streams should be set up as a PTY.
(call_process): Adjust call to 'emacs_spawn'.

* src/process.h (Lisp_Process): Replace 'pty_flag' with 'pty_in' and
'pty_out'.

* src/process.c (is_pty_from_symbol): New function.
(make-process): Allow :connection-type to be a cons cell, and allow
using a stderr process with a PTY for stdin/stdout.
(create_process): Handle creating a process where only one of stdin or
stdout is a PTY.

* lisp/eshell/esh-proc.el (eshell-needs-pipe, eshell-needs-pipe-p):
Remove.
(eshell-gather-process-output): Use 'make-process' and set
':connection-type' as needed by the value of 'eshell-in-pipeline-p'.

* lisp/net/tramp.el (tramp-handle-make-process):
* lisp/net/tramp-adb.el (tramp-adb-handle-make-process):
* lisp/net/tramp-sh.el (tramp-sh-handle-make-process): Don't signal an
error when ':connection-type' is a cons cell.

* test/src/process-tests.el
(process-test-sentinel-wait-function-working-p): Allow passing PROC
in, and rework into...
(process-test-wait-for-sentinel): ... this.
(process-test-sentinel-accept-process-output)
(process-test-sentinel-sit-for, process-test-quoted-batfile)
(process-test-stderr-filter): Use 'process-test-wait-for-sentinel'.
(make/process/test-connection-type): New function.
(make-process/connection-type/pty, make-process/connection-type/pty-2)
(make-process/connection-type/pipe)
(make-process/connection-type/pipe-2)
(make-process/connection-type/in-pty)
(make-process/connection-type/out-pty)
(make-process/connection-type/pty-with-stderr-buffer)
(make-process/connection-type/out-pty-with-stderr-buffer): New tests.

* test/lisp/eshell/esh-proc-tests.el (esh-proc-test--detect-pty-cmd):
New variable.
(esh-proc-test/pipeline-connection-type/no-pipeline)
(esh-proc-test/pipeline-connection-type/first)
(esh-proc-test/pipeline-connection-type/middle)
(esh-proc-test/pipeline-connection-type/last): New tests.

* doc/lispref/processes.texi (Asynchronous Processes): Document new
':connection-type' behavior.
(Output from Processes): Remove caveat about ':stderr' forcing
'make-process' to use pipes.

* etc/NEWS: Announce this change (bug#56025).