What resource do active skills consume?

Every active skill you cast spends EP, so a team that casts often runs dry unless something is feeding it back. That is the job of the Regen role: supports built around restoring energy points to the team, which speeds up recovery and cuts into skill cooldowns.

EP shows up in more than one place. There is a party maximum, and Somniwing's trait raises it by 10 while Somniwing is in the party. There is also ultimate energy, which is tracked separately; some refills restore both, as Leafy's Vitality Blooms do for Grass teammates.

Supports that restore EP generally scale with the Regen stat, so that is the stat to invest in when energy is the problem.

Which Aniimo refill EP

Besauce restores energy without any element condition, so it works on any team. Somniwing's ultimate gives back 50 EP and can top you up mid-rotation, and it fits almost any team too. Leafy's Vitality Blooms circle regenerates about 2.4 EP per second, but only for Grass teammates standing inside it. Luminel's Lightning Surge restores 25.7% of allies' energy, and Livi earns its slot mainly through an EP restoration skill.

The linked guide to EP regen supports covers how to build and choose between them.