If I create the comint buffer myself and then make that inline python function call in the org document, then it works. Below is the lisp I evaluated to make the comint buffer myself based on what I saw in the Backtraces.
(python-shell-make-comint "python" "python-chain" nil)

Here is the Backtrace where I tried to compare what happens when I need to press C-g.
#+begin_example C-c C-c needs to make comint shell
Debugger entered--returning value: 0
  alist-get(yas--post-command-handler ((python-shell-font-lock-post-command-hook . 0) (yas--post-command-handler . 0) (company-post-command . 0) (company-post-command . 0) (yas--post-command-handler . 0) (vertico--exhibit . -90) (consult--preview-post-command . 0) (vertico--exhibit . -90) (eldoc-schedule-timer . 0) (eldoc-schedule-timer . 0) (eldoc-schedule-timer . 0) (eldoc-schedule-timer . 0) (eldoc-schedule-timer . 0) (python-shell-font-lock-post-command-hook . 0) (jit-lock--antiblink-post-command . 0) (company-post-command . 0) (company-post-command . 0) (yas--post-command-handler . 0) (yas--post-command-handler . 0) (company-post-command . 0) (yas--post-command-handler . 0) (vertico--exhibit . -90) (vertico--exhibit . -90) (consult--preview-post-command . 0) (vertico--exhibit . -90) (vertico--exhibit . -90) (consult--preview-post-command . 0) (vertico--exhibit . -90) (vertico--exhibit . -90) (company-post-command . 0) (yas--post-command-handler . 0) (hl-line-highlight . 0) (magit-section-update-highlight . 90) (vertico--exhibit . -90) (vertico--exhibit . -90) (company-post-command . 0) (yas--post-command-handler . 0) (magit-section-update-highlight . 90) (consult--preview-post-command . 0) (vertico--exhibit . -90) (company-post-command . 0) (yas--post-command-handler . 0) (magit-section-update-highlight . 90) (company-post-command . 0) (yas--post-command-handler . 0) (magit-section-update-highlight . 90) (vertico--exhibit . -90) (consult--preview-post-command . 0) (vertico--exhibit . -90) (eldoc-schedule-timer . 0) ...) 0 nil eq)
,* #f(compiled-function (f1 f2) #<bytecode -0x6149ed0fee718f2>)(yas--post-command-handler python-shell-font-lock-post-command-hook)
,* add-hook(post-command-hook python-shell-font-lock-post-command-hook nil local)
  python-shell-font-lock-turn-on()
  inferior-python-mode()
  python-shell-make-comint("python" "python-chain" nil)
  run-python("python")
  org-babel-python-initiate-session-by-key("python-chain")
  org-babel-python-initiate-session("python-chain")
  org-babel-execute:python("print(\"testing12\", end=\"\")" ((:colname-names) (:rowname-names) (:result-params "replace" "output") (:result-type . output) (:results . "replace output") (:exports . "results") (:tangle . "no") (:hlines . "no") (:noweb . "no") (:cache . "no") (:session . "python-chain")))
  org-babel-execute-src-block(nil ("python" "print(\"testing12\", end=\"\")" ((:results . "output replace") (:exports . "results") (:session . "python-chain") (:cache . "no") (:noweb . "no") (:hlines . "no") (:tangle . "no")) nil nil 360 "(ref:%s)"))
  org-ctrl-c-ctrl-c(nil)
  funcall-interactively(org-ctrl-c-ctrl-c nil)
  command-execute(org-ctrl-c-ctrl-c)

#+end_example

#+begin_example comint shell already exists
Debugger entered--entering a function:
,* comint-snapshot-last-prompt()
,* comint-send-string(#<process python-chain> "__PYTHON_EL_eval(\"try:\\n    with open('/var/folder...")
  python-shell-send-string("try:\n    with open('/var/folders/kf/zdpzgs9d30b3jj...")
  org-babel-python--send-string("*python-chain*" "with open('/var/folders/kf/zdpzgs9d30b3jj4bdkdjf1v...")
  org-babel-python-evaluate-session("*python-chain*" "print(\"testing12\", end=\"\")" output ("replace" "output"))
  org-babel-python-evaluate("*python-chain*" "print(\"testing12\", end=\"\")" output ("replace" "output") nil)
  org-babel-execute:python("print(\"testing12\", end=\"\")" ((:colname-names) (:rowname-names) (:result-params "replace" "output") (:result-type . output) (:results . "replace output") (:exports . "results") (:tangle . "no") (:hlines . "no") (:noweb . "no") (:cache . "no") (:session . "python-chain")))
  org-babel-execute-src-block(nil ("python" "print(\"testing12\", end=\"\")" ((:results . "output replace") (:exports . "results") (:session . "python-chain") (:cache . "no") (:noweb . "no") (:hlines . "no") (:tangle . "no")) nil nil 360 "(ref:%s)"))
  org-ctrl-c-ctrl-c(nil)
  funcall-interactively(org-ctrl-c-ctrl-c nil)
  command-execute(org-ctrl-c-ctrl-c)

#+end_example