I think the tag discussion begins with creating distinct character voices, whether that be through cadence, pov, use of slang or other identifier.
And then...
Tags are also about rhythm.
This.
Pacing is so important to the flow of dialogue, and scenes in general. For example, description can rob a conversation of its emotion, but a simple back and forth may sound too much like a Gilmore Girl's script, regardless of tags. The trick is to weave in the action beats, establish mood and keep the characters aware of their surroundings while maintaining the focus on the emotional dynamics. And, as much as possible, have the descriptions and action beats reinforce the mood and flow of the conversation.
I think fewer tags is always better. When necessary, I mostly use 'says', but I think the occasional 'shout', 'mumble' or 'whisper' or whatever works too. I also think adverbs are fine, again, with limited use. Sometimes the strongest verb just doesn't work.
Combining dialog with action beats also helps with the flow.
"No," she said as she turned away. And then change up the structure.
"No," she said, turning away.Another way to improve conversational tension is to avoid monologues. Use shorter sentences, have characters interrupt one another, have them repeat stuff, have them finish each other's sentences, stuff like that (as long as it's in character). So instead of a long paragraph of dialogue, we get a tennis match. And we can vary the pacing by how long or short the responses are. Additionally, if they are discussing something momentous, the conversation can be paused for effect. The characters can stop to observe one another, think about a related thing (foreshadowing/call back/metaphor), or we can insert an action beat or description before the conversation resumes.
The conversation can also be paused at the proper time or interrupted by external events: someone walking into the room, a geographic obstacle requiring all of their attention or some other action setup, which can build tension. Leaving stuff unfinished "for now" is a great story tool, just don't make the reader keep track of too many balls in the air at once.
All of these options reduce the need for dialogue tags.
But it all gets more complicated when we have three or more people in the conversation. And even though most of the above still holds true, you really need to identify every speaker here, one way or the other, except when it's a direct response made obvious from the preceding dialogue. Otherwise it can get confusing fast.
Oh, one more thing. When several people are in a conversation, try not to lose sight of the ones not speaking. They can become invisible to the reader. So even if they aren't talking, have them react to the conversation or do something so we don't forget they're there.