What stats do support Aniimo scale with?

The stat to build follows the individual Aniimo, not the word "support" on its role. Two supports on the same team can want completely different things: HP for one whose healing grows with it, Regen for one whose regen effects grow with it, Attack for a third. Read what each one actually does before you pour resources into a stat.

Roles are fixed and cannot be changed, so the stat question is always about the Aniimo you already have. If a healer like Glacy or Gracewing is filling your healer slot, its HP or Regen matters more than its damage output. Flutternym is a useful contrast: its reserve heal restores 0.5% of the active Aniimo's maximum HP whenever teammates use skills or Ultimates, so that heal is measured against whoever is on the field, not against Flutternym.

A support that scales with Attack still exists to make the team hit harder, not to top the damage chart. Its buffs do the most when timed around the break window and reapplied just before the break gauge empties, so your damage dealer's burst lands fully buffed. That is also why a player without a strong, leveled damage dealer, for example under 3000 CP, can still pull weight in multiplayer on a support or breaker.