brew doctor
should give you some hints.
I just did a fresh installation for my Apple M1, seems just working fine without any additional setup.
$ brew install node
==> Downloading https://ghcr.io/v2/homebrew/core/c-ares/manifests/1.18.1
######################################################################## 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/c-ares/blobs/sha256:7b1eacc9efbe8ac32a4a
==> Downloading from https://pkg-containers.githubusercontent.com/ghcr1/blobs/sha256:7b1e
######################################################################## 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/libuv/manifests/1.42.0
######################################################################## 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/libuv/blobs/sha256:7b0a2b27ac3b806ff9e59
==> Downloading from https://pkg-containers.githubusercontent.com/ghcr1/blobs/sha256:7b0a
######################################################################## 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/node/manifests/17.2.0
######################################################################## 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/node/blobs/sha256:f3efe9900c885d5bcc3a39
==> Downloading from https://pkg-containers.githubusercontent.com/ghcr1/blobs/sha256:f3ef
######################################################################## 100.0%
==> Installing dependencies for node: c-ares and libuv
==> Installing node dependency: c-ares
==> Pouring c-ares--1.18.1.arm64_monterey.bottle.tar.gz
/opt/homebrew/Cellar/c-ares/1.18.1: 87 files, 665.3KB
==> Installing node dependency: libuv
==> Pouring libuv--1.42.0.arm64_monterey.bottle.tar.gz
/opt/homebrew/Cellar/libuv/1.42.0: 49 files, 3.5MB
==> Installing node
==> Pouring node--17.2.0.arm64_monterey.bottle.tar.gz
==> Caveats
Bash completion has been installed to:
/opt/homebrew/etc/bash_completion.d
==> Summary
/opt/homebrew/Cellar/node/17.2.0: 2,018 files, 44.4MB
==> Running `brew cleanup node`...
Disable this behaviour by setting HOMEBREW_NO_INSTALL_CLEANUP.
Hide these hints with HOMEBREW_NO_ENV_HINTS (see `man brew`).
==> Caveats
==> node
Bash completion has been installed to:
/opt/homebrew/etc/bash_completion.d
$ ls -al /opt/homebrew/bin/node
lrwxr-xr-x 1 ruichen admin 30 Dec 13 15:56 /opt/homebrew/bin/node -> ../Cellar/node/17.2.0/bin/node
$ node --version
v17.2.0