Weirdly, many of the published Traveller campaigns for Mongoose Traveller are... exploration or discovery. Deepnight Revelation. The Rim Expeditions. Even the "Ancients trilogy" is, so far, about discovery and mystery. Granted, it sounds like it is heading towards some kind of war. "Whispers from the Abyss" sounds like a "discover new things" campaign, not a trade or war campaign. Prometheus is neither trade nor war, but I suppose it isn't really exploration or discovery either.
Skandersvik is a trade campaign, admittedly.
I guess if you squint, Pirates of Drinax counts as "trade and war", but I doubt that is what most folks think of when you say that.
Next year, we are getting a war thing. But we are also getting Singularity, which is a paradigm changing campaign from what it sounds like. And Pioneer, which is seems likely to involve exploration and stuff.
I don't understand this view that Traveller is narrow and constraining. Even the Charted Space setting isn't constrained. You can do all kinds of exploration and discovery in the setting. And if you want to go full warp speed, you can easily use different tech assumptions like Mindjammer does. No one playing Traveller is limited to the Charted Space setting.