As a former long-time Gentoo user, I use Arch 😉

There is no direct equivalent, system32 is just a collection of libraries, exes, and confs.

Some of what others have said is accurate, but to explain a bit further:

Longer explanation:
::: spoiler spoiler
system32 is just some folder name the MS engineers came up back in the day.

Linux on the other hand has many distros, many different contributors, and generally just encourages a .. better .. separation for types of files, imho

The linux filesystem is well defined if you are inclined to research more about it.
Understanding the core principals will make understanding virtually everything else about "linux" easier, imho.

https://tldp.org/LDP/intro-linux/html/sect_03_01.html

tl;dr; "On a UNIX system, everything is a file; if something is not a file, it is a process."
:::

The basics:

• /bin - base level executables, ls, mv, things like that
• /sbin - super-level-only (root) executables, parted, reboot, etc
• /lib - Somewhat self-explanatory, holds libraries, lots of things put their libs here, including linux kernel modules, /lib/modules/*, similar to system32's function of holding critical libraries
• /etc - Configuration lives here, generally speaking, /etc/<application name> can point you in the right direction, typically requires super-user (root) to edit
• /usr - "User installed" software, which can be a murky definition in today's world, but lots of stuff ends up here for installed software, manuals, icon files, executables

Bonus:

• /opt - A special location, generally third-party, bundled-style software likes to use this, Java for instance, but historically some admins use it as the "company location", meaning internally developed software would live there.
• /srv - Largely subjective, but myself and others I know use it for partitions that are outside the primary disk, for instance we use /srv/db for database volumes, /srv/www for web-data volumes, /srv/Media for large-file storage, etc, etc

For completeness:

• /home - You'll find your user directories here, personally, this is my directory I backup, I don't carry much more with me on most systems.
• /var - "Variable data", basically meaning any data that will likely grow over time, eg: /var/log