There's no official installer for this, but the following approach works reliably.
For a system-wide install, avoid install.sh, since it hardcodes a per-user PNPM_HOME. Instead, download the standalone @pnpm/exe binary to a shared location and symlink it into /usr/local/bin:

curl -fsSL https://github.com/pnpm/pnpm/releases/latest/download/pnpm-linuxstatic-x64 -o /opt/pnpm/pnpm
chmod +x /opt/pnpm/pnpm
ln -s /opt/pnpm/pnpm /usr/local/bin/pnpm

If Node.js is already installed system-wide, corepack enable is also an option and makes pnpm available on PATH for all users without any per-user configuration.

Regarding a shared store for global installs: pnpm doesn't have a built-in "system store" separate from the user store, but you can approximate this by setting global-dir and global-bin-dir system-wide (e.g. via environment variables in /etc/profile.d/pnpm.sh), pointing to a shared location such as /opt/pnpm/global. Anyone who needs to install or update global packages requires write access to that directory; other users can still use the resulting binaries via PATH.

This was discussed previously in #5007, with the same conclusion: it works if global-dir/global-bin-dir and permissions are configured explicitly, but there is no dedicated "system store" concept built into pnpm.

There is no official system-wide installer and no supported multi-user shared store, so this ends up being assembled from parts.

For the binary itself the clean option is the standalone build: drop it in /opt/pnpm/pnpm and symlink it into /usr/local/bin. It has no Node dependency, so service accounts can run it without any per-user setup. If you already manage a system-wide Node install, corepack enable pnpm run from a root shell places shims next to the node binary, which achieves the same thing and keeps the version pinned via the packageManager field of your projects.

The store is the tricky part. By default each user gets their own store under their XDG data dir, and pnpm expects to own it. You can point everyone at a shared location by setting storeDir (env NPM_CONFIG_STORE_DIR in /etc/profile.d/ works for interactive users, or set it in each service's unit file), but be aware of what you are signing up for: files land owned by whichever user wrote them first, packages are hard-linked from the store so it must sit on the same filesystem as the projects, and you need a shared group plus a sane umask for writes not to fail. It works, people run it, but permissions problems are yours to manage.

For service accounts specifically I would honestly skip the shared store and let each service user keep its own. The store is content-addressed, so the duplication is bounded, and you avoid the whole class of "installed fine as user A, EACCES as user B" issues.