Neovim

The terminal does not have a filetype, but it does has buftype=terminal. There is also a dedicated autocmd TermOpen where you can set up your settings as you want.

I feel somehow similar, also using tmux (in my case inside st terminal) and neovim. I tried various times combining the features of the terminal and tmux but I am so used to the very specific workflows I developed over the years that I've thus far always come back to that setup.

And here is the part that might relate to you: is there any explicit pain you experience with your current setup or would it be just nice/cool/nerdy to be able to combine things? In the latter case my experience is: leave it as it is and save this time for some more productive improvements. :-)

I use neovim-session-manager plus lspsaga’s floating terminal window that opens a terminal in pwd together to do that kinda stuff, plus remapping some commands in terminal mode to help me exit easily because the default command is awkward for me to hit. Here’s my config, lmk if you want to be pointed at any specific part cause it’s kinda funky https://github.com/avegancafe/Juliet

I also use tmux and neovim in my workflow, but I actually prefer it that way.

I think it's good to have that separation of responsibility.
Tmux handles the work sessions, nvim handles text editing.