org-mode/babel and zsh: Getting shell sessions to work

Question

I've been trying to get shell code blocks with sessions to work, but not entirely succeeding.

My setup: emacs 26.1 (spacemacs) org-mode 9.2.2 default shell: zsh 5.7.1

Everything seems to work fine with sh but it fails with shell.

Ordinary, non-session execution works:

#+begin_src shell
  echo ${TERM}
  echo ${0}
#+end_src

#+RESULTS:
| dumb         |
| /usr/bin/zsh |

However, when I try to add a session I don't get the result I expect

#+begin_src shell :session s1
  FOO=bar
  echo ${TERM}
  echo ${0}
#+end_src

#+RESULTS:
|                                                       |
| magthecomp% 

[?2004hmagthecomp% FOO=bar[?2004l |

and on further use of that session emacs freezes up and I have to interrupt it (<Ctrl-g>), for instance if I try to execute

#+begin_src shell :session s1
  echo ${FOO}
#+end_src

When I take a look at the session buffer I see the following after running those blocks

FOO=bar
magthecomp% echo ${TERM}
magthecomp% FOO=bar
echo ${0}
echo ${0}
echo 'org_babel_sh_eoe'
echo 'org_babel_sh_eoe'
magthecomp% echo ${TERM}echo ${0}
dumbecho /usr/bin/zsh
            echo 'org_babel_sh_eoe'
org_babel_sh_eoe
magthecomp% echo ${FOO}
echo ${FOO}echo 'org_babel_sh_eoe'
            echo ${FOO}echo 'org_babel_sh_eoe'

(some colour is lost when copying it)

I already toned down the theme for my shell prompt when ${TERM} == "dumb", but apparently that isn't enough. Any pointers on how to adjust my zsh config to make it work would be much appreciated.