Don't round-trip auto-reconnect probe in ERC

Don't round-trip auto-reconnect probe in ERC

* lisp/erc/erc-backend.el (erc-server--reconnect-opened)
(erc--server-reconnect-opened): Rename former to latter.  Restore
original buffer-local value of session connector for Emacs 29 and below.
(erc--server-reconnect-timeout-check)
(erc--server-reconnect-timeout-scale-function): Change from buffer-local
to normal variables, which they should have been originally.
(erc--recon-probe-reschedule): Ensure `erc-server-reconnect-timeout' is
always non-nil to avoid seeing format specifier in admin message.  Use
current buffer when `proc' argument is nil.  Perform cleanup when `proc'
and `erc-server-process' differ.
(erc-server-delayed-check-reconnect-reuse-process-p): New variable.
(erc--recon-probe-sentinel): Run `erc--server-reconnect-opened'
immediately because sending a speculative PING doesn't work on all
servers and proxies, most crucially on ZNC, which replies with an error
only after an extended timeout.
(erc--recon-probe-filter): Remove unused function.
(erc--recon-probe-check) Rework to not use fixed periodic timer, change
second parameter to a Lisp time object.
(erc-server-delayed-check-reconnect): Use realistic name when reusing
process so that the session's process isn't "*erc-connectivity-check*".
Set filter to `ignore'.  Always run `erc--recon-probe-sentinel' when
status is `open' or something other than `connect', but don't bother
spawning a `erc--recon-probe-check' task as well because any problems
creating the process should already be known.  Handle quits during
connect functions that perform blocking I/O, such as
`socks-open-network-stream'.
(erc-schedule-reconnect): Don't bother setting filter to nil.
* test/lisp/erc/erc-scenarios-base-auto-recon.el
(erc-scenarios-base-auto-recon-unavailable)
(erc-scenarios-base-auto-recon-check/no-reuse): Rename former to latter.
(erc-scenarios-base-auto-recon-no-proto)
(erc-scenarios-base-auto-recon-check/reuse): Rename former to latter and
rewrite not to expect a PING.
* test/lisp/erc/resources/erc-d/erc-d.el (erc-d--forget-process): New
function.
(erc-d--process-sentinel): Stop serving when all dialogs have been
exhausted.  (Bug#62044)

(cherry picked from commit c0cb59578b5aeb75b4856dda518d80cd015caa7d)