Your Stamina cap goes up by feeding Lumin Amber into a Breezy Plains Branch, and maxing it out even removes the Stamina cost of moving around outside of combat. Here's how it works and where to find Lumin Amber.
How to Increase Your Stamina Cap
The main way to raise your Stamina cap is to take Lumin Amber you've collected to the Breezy Plains Branch. Feeding Lumin Amber into the Branch raises its Infused count, and reaching certain milestones unlocks nodes with permanent bonuses. For example, the New Vigor node unlocks at 20 Infused and increases your Stamina cap by 10%.
Some of the Branch's other nodes reduce how much Stamina you spend while exploring the Breezy Plains, on top of the cap increases.
How to Get Infinite Stamina in Breezy Plains
Keep feeding the Breezy Plains Branch and you'll eventually reach the Wanderer's Might node at 150 Infused. Past that point, moving around the Breezy Plains out of combat no longer costs Stamina at all.
Where to Get Lumin Amber
The Lumin Amber used at the Breezy Plains Branch is officially named Lumin Amber: Breezy Plains, described in-game as amber infused with Lumin power that the Branches in Breezy Plains can absorb to grow.
Lumin Amber is scattered around the map. You can find it in Sanctums, as a completion reward from exploration puzzles, as a first-clear reward from Alpha and Omega Challenges, and from event rewards.