In tmux, can I color different pane borders & titles differently?

Ouch, yes, that's a pane (pun intended). pane-border-format and pane-border-style are server options, not pane options.

As such, you have to come up with one style or format that handles all your use cases. That starts to become a nested mess of conditionals pretty quickly. With three panes, it's workable, but it ain't pretty.

I'm going to format this as a multiline to start with for readability. You'll want to remove the extra whitespace when using it in practice since the whitespace does get displayed:

tmux set pane-border-format " #{?#{==:#{pane_title},remote_development}, #[fg=white bg=green], #{?#{==:#{pane_title},quality_assurance}, #[fg=black bg=yellow], #{?#{==:#{pane_title},production}, #[fg=white bg=red], #[default] } } } #{pane_index} #{pane_title} " 

It's basically a nested conditional that matches the pane title against the ones you list, and then sets the colors you mentioned before displaying the index and title. I took out the normal "reverse" indicator for the active pane since it would have (I believe) have required an entire new nesting level, but you can add some other indicator if you want.