If I play Phoebe while my opponent has a Dunsparce with "Mysterious Nest" Ability in play, do my Pokemon VMAX's attacks calculate Weakness if applicable or not?
The term "any effects" does not include effects that alter Weakness and Resistance. So Phoebe does not allow you to ignore Mysterious Nest's effect.
Source: TPCi Rules Team (2022-05-05)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH8_207
SWSH8_207
SWSH5_130
SWSH5_130