I basically took the general idea from this Ubuntu doc and made som changes. After installing debootstrap, I followed these general steps:

• set up an user for Steam, with adduser steam.
• created a directory to host the "virtual machine" at /var/lib/chroot/steam64.
• used the page linked above to create a schroot profile directory with the chroot data I want.
• used the page linked above to create a schroot profile entry for the chroot, adding steam as one of its allowed users.
• set up an Ubuntu 18.04 schroot with the following command: debootstrap --variant=buildd bionic /var/lib/chroot/steam64 http://archive.ubuntu.com/ubuntu/
• on the host, allowed cross-"host" applications to lauch windows with xhost +local:.
• once completed, entered the schroot as root and added the needed i386 arch and packages for Steam and for bubblewrap / Chrome containerization.
• still in the schroot as root, installed enough packages for a basic graphical environment (basically: a text editor, xnest and xterm; between their dependencies, they'll take care of most of everything).
• exited the schroot.
• entered the schroot as steam and fired up the Steam launcher manually.

It's not perfect, there are a few issues (in particular with audio) but once I had the installed schroot ready, I never had to worry about its 32-bit packages ever again. And that was back in.... like, 2019 or something. Six months ago I copied to old schroot to my new machine and resumed playing, with no more cost than having to set up the schroot packages and the steam user (with the same old UID) on the new machine.

Here's a sample of the schroot profile file I'm using. The "steam64.local" is the profile directory, which is basically a copy of schroot/buildd (or of schroot/minbase) with some configurations in fstab and copyfiles to account for eg.: isolating /var/run and dbus, and giving the schroot access to the home directory for the steam user.