The bug
When the entity inflicting the damage in the /damage command is a spectral arrow or tipped arrow, the status effect and on fire status of the spectral arrow or tipped arrow will not be applied.
Reproduce steps
Summon a skeleton.
Shoot the spectral arrow or tipped arrow on the ground with a bow.
Use the following command:
Tipped arrow
/damage @p 1 minecraft:arrow by @e[type=minecraft:arrow,limit=1] from @e[type=minecraft:skeleton,limit=1]
Spectral arrow
/damage @p 1 minecraft:arrow by @e[type=minecraft:spectral_arrow,limit=1] from @e[type=minecraft:skeleton,limit=1]
Found that no status effect was caused after the damage was done.
Confirmed.