I don't know which Klingons you've been watching, but the ones with cloaking devices and using VISORs to obtain shield frequencies definitely stab people in the back. "In war, there is nothing more honorable than victory"
She needed stopping power to try to stop him from killing her captain - you don't fire the taser equivalent at the person killing your superior officer, you fire your most powerful weapon - the 'kill' setting. Plus, Burnham doesn't necessarily know that's the leader, they've never met and I don't think she was on the bridge when he did his video link to threaten them.
Star trek's done that trope since forever. Bit harsh to cite Discovery for doing it.