I've noticed that IS does a weird thing when dropping healers in the summon pool. Earlier this year when they reran the Bridal Blessings banner, I got a Bridal Lyn with Candlelight equipped out the box. fast forward to CYL2, I got a Brave Veronica however Hliðskjálf was not equipped. Additionally, while browsing their character pages on this site, I learned that togglng weapon might doesn't factor into Veronica but does on Halloween Mia for example. Do you think IS does it this way because some staff units are seasonal and others are always in the pool? That's how it appears to me.
I'm not on how they do healers anymore honestly I'm pretty sure my Veronica started off with her Weapon already equipped, I know that healers in the 3-4* poll don't start off with a staff not sure on 5* healers never got any besides Genny and that was a long time ago so I don't remember if she did or not
Pokemon GO
Fire Emblem Heroes
Fate Grand Order
Dragonball Legends
Dragalia Lost
IV Calc
Heroes