The green female Byleth represents Sothis, a green-haired girl who uses Byleth as a vessel and appears as part of their Progenitor God Ruptured Heaven Final Smash.
The stage's background represents the darkness of Byleth's consciousness where they first encounter Sothis in the tenth chapter of Fire Emblem: Three Houses.
The Health Recovery rule references the Divine Pulse, a skill granted to Byleth by Sothis, which allows them to rewind turns in battle, which will restore their HP at a certain point.
Other trivia:
This spirit's Support type references Sothis' role as Byleth's ally in Three Houses.
This spirit's Critical-Health Healing ↑ ↑ ability further references the Divine Pulse skill, which allows Byleth to rewind turns in battle, which will restore their HP at a certain point.