alt Hacker NewsBrew got one thing right that no Linux package manager seems to emulate: it doesn't require root for normal operations and even goes so far as to error out if running as root (https://docs.brew.sh/FAQ#why-does-homebrew-say-sudo-is-bad).
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"let's allow any user process to modify my binaries" is not something to be proud of...
It needs world-writtable /opt/homebrew, so I guess a Linux equivalent would be Nix (which IIUC requires writable /nix).
For something that only uses your home folder, I recommend checking out mise https://mise.jdx.dev/
Brew _is_ a linux package manager.
There is also conda/mamba/pixi/etc. (anything in the conda-forge ecosystem) that can be used without root. Then there are Guix and nix, which (mostly) require to be set up by someone with root privileges, but which then allow unprivileged users to install packages for themselves. I think I have even used emerge rootless-ly at some point a few years ago.
Brew is so full of Linux/OSS/GNU anti-patterns that I can't wrap my head how did it ever managed to receive so much adoption. I guess macOS people are way more ignorant about things that made Linux/OSS what it is.