I just setup erlang 25.0.3 and elixir 1.13.4 on my m1 mbp using asdf package manager without any issue. Observer works flawlessly.
There was an issue with wxwidgets 3.1.x which is now resolved in latest version 3.2.x
I followed following steps

brew install kerl
brew install wxwidgets

.kerlrc in ~

KERL_CONFIGURE_OPTIONS="--disable-debug --without-javac --enable-dynamic-ssl-lib --enable-shared-zlib --enable-hipe --enable-smp-support --enable-threads --enable-kernel-poll --with-wx"
KERL_BUILD_DOCS=yes

installed eralng and elixir

asdf install erlang 25.0.3
asdf global erlang 25.0.3

asdf install elixir 1.13.4-otp-25
asdf global elixir  1.13.4-otp-25

This works for me:

$ KERL_CONFIGURE_OPTIONS="--disable-debug --disable-silent-rules --without-javac --enable-shared-zlib --enable-dynamic-ssl-lib --enable-threads --enable-kernel-poll --enable-wx --enable-webview --enable-darwin-64bit --enable-gettimeofday-as-os-system-time --with-ssl=/opt/homebrew/opt/openssl@3" asdf install erlang 25.0.2

❯ sysctl -a | grep machdep.cpu
machdep.cpu.cores_per_package: 10
machdep.cpu.core_count: 10
machdep.cpu.logical_per_package: 10
machdep.cpu.thread_count: 10
machdep.cpu.brand_string: Apple M1 Max

The options came from a tweet of Jose, one I cannot seem to find quickly

I wrote that Stack Overflow answer, and I can still build OTP 25 on an M1 Mac using those instructions.

There is not much info in the logs you provided. Is there not a more detailed log that tells you more information about whats going wrong?

My guess is you skipped a step listed in the make sure to read the "Before asdf install" point.

Actually I’m having problems myself recently building with asdf-erlang with KERL_BUILD_DOCS set, which I wrote about here. However, it works when I use kerl directly, not asdf. I wonder if your error is related? There could be an asdf bug.

Unfortunately building Erlang is a complex process and there are readmes to be read and choices to be made. The foolproof “just do this” ways are good until they break, then you’re back to reading readmes and setting environment variables anyway.