Shingi understood those auras represented the person's HP, SP, and MP. Red represented HP, green SP, and blue the MP. Syra didn't have any SP since she was a spirit, so she didn't have a Stamina Aura.
Shingi wasn't sure why he couldn't see them before that moment, but he was glad he could do so. He hadn't been recruited in the party, as he didn't want to earn any exps through it to be sure he wouldn't level up.
But he couldn't tell how much HP or MP everyone had at the same time. He could open the Status Window of his students to check, but it wasn't instant, as it took a couple of seconds, and it would also block somewhat his vision as a full panel would appear in front of him.
Since he had the most experience, he usually was in charge of ordering people, depending on their current state. When they recruited him, he could see their HP, MP, and SP bar over them if he focused on them, but that wasn't an option if one wasn't at the party that recruited him.