Reimplement `backtrace-on-redisplay-error` using `push_handler_bind`.
This moves the code from `signal_or_quit` to `xdisp.c` and
`debug-early.el`.

* lisp/emacs-lisp/debug-early.el (debug-early-backtrace):
Add `base` arg to strip "internal" frames.
(debug--early): New function, extracted from `debug-early`.
(debug-early, debug-early--handler): Use it.
(debug-early--muted): New function, extracted (translated) from
`signal_or_quit`; trim the buffer to a max of 10 backtraces.

* src/xdisp.c (funcall_with_backtraces): New function.
(dsafe_calln): Use it.
(syms_of_xdisp): Defsym `Qdebug_early__muted`.

* src/eval.c (redisplay_deep_handler): Delete var.
(init_eval, internal_condition_case_n): Don't set it any more.
(backtrace_yet): Delete var.
(signal_or_quit): Remove special case for `backtrace_on_redisplay_error`.
* src/keyboard.c (command_loop_1): Don't set `backtrace_yet` any more.
* src/lisp.h (backtrace_yet): Don't declare.

Make sure we build the (ERROR-SYMBOL . ERROR-DATA) object only once
when signaling an error, so that its `eq` identity can be used.
It also gets us a tiny bit closer to having real "error objects"
like in most other current programming languages.

* src/eval.c (maybe_call_debugger): Change arglist to receive the error
object instead of receiving the signal and the data separately.
(signal_or_quit): Build the error object right at the beginning so it
stays `eq` to itself.
Rename the `keyboard_quit` arg to `continuable` so say what it does
rather than what it's used for.
(signal_quit_p): Change arg to be the error object rather than just the
error-symbol.

* src/keyboard.c (cmd_error_internal, menu_item_eval_property_1):
Adjust calls to `signal_quit_p` accordingly.

* test/src/eval-tests.el (eval-tests--error-id): New test.

Rather than blindly increase `max-lisp-eval-depth` when entering the
debugger or running `signal-hook-function`, use this new "reserve"
to keep track of how much we have grown the stack for "debugger"
purposes so that for example recursive calls to `signal-hook-function`
can't eat up the whole C stack.

* src/eval.c (max_ensure_room): Rewrite.
(restore_stack_limits): Move before `max_ensure_room`.  Rewrite.
(call_debugger, signal_or_quit): Adjust calls accordingly.
Also grow `max-lisp-eval-depth` for `hander-bind` handlers.
(init_eval_once): Don't initialize `max_lisp_eval_depth` here.
(syms_of_eval): Initialize it here instead.
Add new var `lisp-eval-depth-reserve`.

* doc/lispref/eval.texi (Eval): Add `lisp-eval-depth-reserve`.

`macroexp--with-extended-form-stack` used manual push/pop so that upon
non-local exits the "deeper" value is kept, so the error handler gets
to know what was the deeper value, so as to be able to compute more
precise error locations.
Replace this with a `handler-bind` which catches that "deeper" value
more explicitly.

* lisp/emacs-lisp/bytecomp.el (bytecomp--displaying-warnings):
Use `handler-bind` to catch the value of `byte-compile-form-stack`
at the time of the error.  Also consolidate the duplicated code.

* lisp/emacs-lisp/macroexp.el (macroexp--with-extended-form-stack):
Use a plain dynbound let-rebinding.

Move ad-hoc code meant to ease debugging of bootstrap (and batch mode)
to `top_level_2` so it doesn't pollute `signal_or_quit`.

* src/lisp.h (pop_handler, push_handler_bind): Declare.
* src/keyboard.c (top_level_2): Setup an error handler to call
`debug-early` when noninteractive.
* src/eval.c (pop_handler): Not static any more.
(signal_or_quit): Remove special case for noninteractive use.
(push_handler_bind): New function, extracted from `Fhandler_bind_1`.
(Fhandler_bind_1): Use it.
(syms_of_eval): Declare `Qdebug_early__handler`.
* lisp/emacs-lisp/debug-early.el (debug-early-backtrace): Weed out
frames below `debug-early`.
(debug-early--handler): New function.

This provides a more reliable fix for bug#65267 since we don't
touch `debug-on-error` nor `debug-ignore-errors` any more.

* lisp/startup.el (startup--debug): New function.
(startup--load-user-init-file): Use it and `handler-bind` instead of
let-binding `debug-on-error`.

That test relied on `debugger` and `debug-on-signal` in a way that
doesn't work with the new ERT code.

* test/src/emacs-module-tests.el (mod-test-non-local-exit-signal-test):
Use `handler-bind` rather than the debugger.

* test/lisp/emacs-lisp/bytecomp-tests.el
(bytecomp-tests--error-frame, bytecomp--byte-op-error-backtrace):
Make test pass again and simplify, using handler-bind instead
of the previous debugger hack.

Now that `ert.el` uses `handler-bind` instead of `debugger`, some
details of the behavior have changed.  More specifically,
three tests are now broken, but these basically tested the failure
of ERT's machinery to record errors when ERT was run within
a `condition-case`.
AFAICT, these tests do not check for a behavior that we want,
so rather than "fix" them, I disabled them.

* test/lisp/emacs-lisp/ert-tests.el (ert-test-error-debug)
(ert-test-fail-debug-with-condition-case)
(ert-test-should-failure-debugging): Comment out.
(ert-test-with-demoted-errors): It now passes.  Bug#11218 is fixed!

* lisp/emacs-lisp/ert.el (ert--should-signal-hook): Delete function.
(ert--expand-should-1): Don't bind `signal-hook-function`.
(ert--test-execution-info): Remove `next-debugger` slot.
(ert--run-test-debugger): Adjust to new calling convention.
Pass the `:backtrace-base` info to the debugger.
(ert--run-test-internal): Use `handler-bind` rather than let-binding
`debugger` and `debug-on-error`.

* lisp/emacs-lisp/ert-x.el (ert-remote-temporary-file-directory): Don't
use `defconst` if it's not meant to stay constant (e.g. we let-bind it
in tramp-tests.el).