I recently came back from a clinic that focused on the breath as an aid: that holding your breath, or at least engaging your diaphragm and holding some (mostly positive) tension in your ribcage encourages the horse to engage their core and pick up their sternum, so use in collected movements (shoulder in, half pass, pirouette work). This may mean taking short shallow "sips" of breath so you don't pass out.
Pushing your breath out like a laser (vs a slow-moving puff) in extensions to keep that engagement through your core while encouraging the horse to reach forward and swing.
A big exhale, like a sigh, directed at the inside ear can help resettle the connection and encourage your horse to soften into it.
And a normal exhale timed with any transition can encourage softness as the horse steps up or down into the next gait.
I'll admit, I walked into this clinic skeptical of the efficacy of breathing. But without any other tweaks to my riding, all of the work got both softer and more engaged with neither of us bracing on the other, when I was consciously using my breath as an aid instead of an afterthought.
I was a competitive brass musician for about a decade, but it turns out that decade was about a decade+ ago, so it was harder than I thought it would be to both monitor my breathing and also sustain for full movements (especially long diagonals, jeez. Impossible).
And if you've made it this far, here's a picture of Queso in a hat:
