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I need a very simple web server on a very small embedded system with a MISP processor. I thought that the simplest server could be a shell script listening to a TCP port.

The problem is that the system doesn't have even perl. Only some basic shell /bin/sh. I searched the web for "how to listen to a port from a shell", but answers I found all referred to some other tools like nc, which I don't have.

Is it even possible to do?

The system, it's a router, has busybox installed and some other binaries in the /bin directory, they are:

#ls /bin
chown df fatattr gzip login mount
ping rm shuf touch usleep
busybox comgt dmesg fgrep hostname ls
mv ping6 rmdir sleep true vi
busybox-new cp echo flock ip mkdir
netstat printf sdparm split umount watch
cat date egrep grep kill mknod
nice ps sed sync uname wget
chmod dd false gunzip ln more
pidof pwd sh tar unlink zcat

And the busybox:

Currently defined functions:
[, arp, ash, awk, basename, busybox, cat, chmod, chown, cp, crond,
cut,date, dd, df, dirname, dmesg, du, echo, egrep, env, expr, false,
fdisk, fgrep, find, free, ftpget, getty, grep, head, hexdump,
hostname, ifconfig, init, insmod, ip, kill, killall, klogd, ln,
login, ls, lsmod, md5sum, mkdir, mknod, mkswap, modprobe, more,
mount, mv, netstat, nslookup, passwd, pidof, ping, ping6, ps, pwd,
readlink, reboot, renice, rm, rmdir, rmmod, route, sed, seq, sh,
sleep, sort, swapoff, swapon, sync, sysctl, syslogd, tail, tar,
taskset, test, tftp, time, top, touch, tr, traceroute, true, udhcpd,
umount, uname, unzip, uptime, usleep, vi, watch, wc, which,
xargs, yes

It has some other stuff too in other locations from the PATH, but no nc, no httpd or something like that

No, a basic Bourne/POSIX shell (/bin/sh) cannot be expected to include any built-in facilities for TCP connections. See comparision of command shells in Wikipedia.

The bash shell would have TCP and UDP client capabilities with a special handling of certain filenames: for example, using /dev/tcp/<hostname>/<port> in input/output redirection on a command line causes bash connect to the specified host and port and use the connection as input source or output destination. But bash cannot listen on a port: it cannot act as a TCP server.

The zsh shell would have both client and server functionality, but only using TCP. On the other hand, zsh is not a simple shell: it's probably the most feature-rich (and so the largest) of the common unix-style shells as far as I know. Finding zsh on a small embedded system would be rather unlikely.

While I was writing my answer, you indicated in the comments that you found a "lighthttpd" binary. Is it perhaps this? https://www.lighttpd.net/