Let's remove objdir entirely and just use obj/.

Not important at all, but REPLACED_OBJS might be a better name to
signify to people reading the makefile what this is about.

It looks like you're missing mkdir rules for everything but $(SRC_DIRS).

Removing the bits symlink is ok, but we need to preserve the logic
that prevents trying to build without ARCH set. Perhaps something
like:

ifeq ($(ARCH),)
$(error Please run configure or set ARCH in config.mak before running make)
endif

just after the inclusion of config.mak.

I suppose this comment was meant to be removed?

Not new in your patch, but I wonder if using $$(cat $<) would make
more sense than $(shell cat $<) -- does the latter risk getting
evaluated even when the rule isn't being run?

> -lib/%.o: crt/%.o
> +lib/%.o: $(objdir)/crt/%.o
>       cp $< $@

I don't see how this gets arch versions of crti.o/crtn.o. I think you
must be producing the dummy ones from the empty .c files, which won't
work. Actually once this is all done the dummy .c files there can
probably be removed, or we could remove them right away to eliminate
the need for another filter-out here (but I don't think that's really
needed anyway since it's a small fixed set of files we can hard-code).

BTW that made me realize one semantic change in how the new build
system treats arch files: src/*/$(ARCH)/*.s (and .sub and whatever
other types we add) will get used now even if there's no .c file by
the same name in the parent directory. This actually looks to be
really nice -- we can eliminate dummy .c files that are empty and only
have them when the generic implementation works for some/most archs.
We can also move the arch/$(ARCH)/src/* files to appropriate
src/*/$(ARCH) locations based on what code they go with.

> +test -f Makefile || ln -sf $srcdir/Makefile .

Is there a reason you do it this way rather than checking for
srcdir=.? The reason I ask is that existence of a stray makefile
that's not a symlink to the musl makefile should probably be an error
here rather than silently ignored. But maybe there are more things to
consider..