This is because for org-mode code blocks highlight you may need to add association of "language identifier" (i.e. the one you're writing like #+begin_src python or #+begin_src go, etc) to the mode.
So in your case:
(add-to-list 'org-src-lang-modes '("go" . go-ts))
Note that -mode postfix is missing. It's because it is appended by org-src-get-lang-mode.
P.S.: I think you can contribute such change to go-ts-mode, so it populates the variable if it's enabled. Or maybe better, contributing a org-src-get-lang-mode change so it takes into account -ts modes, since these days there are many of them.
P.P.S: FYI, I don't even use go nor org modes (I prefer markdown to org-mode and don't even know org-mode syntax). Everything I wrote was inferred in 2 minutes by git-grepping over Emacs sources; in this case I found this Q/A on org syntax-highlight, and then grepped for org-src-fontify-natively. This is the power of open-source: I recommend you to look at source code more often in search for answers 😊
(org-src-get-lang-mode "go")show?