Are the plants animated by an Assassin Vine considered magical

In our last play session the party was attacked by an Assassin Vine. The low-strength kobold ranger was trapped in the vines for several rounds (in part because he went unconscious from damage, but that's beside the point of this question). The party wizard had "Wither and Bloom" but did not use it. However, we are in the jungles of Chult – this was not the first Assassin Vine we have seen and I doubt it will be the last. It would be good to know if we could use Wither and Bloom to free someone if needed.

Wither and Bloom says (emphasis mine):

You invoke both death and life upon a 10-foot-radius sphere centered on a point within range…Nonmagical vegetation in that area withers.

The Assassin Vine's Entangling Vines feature says (emphasis mine):

The assassin vine can animate normal vines and roots on the ground in a 15-foot square within 30 feet of it. These plants turn the ground in that area into difficult terrain. A creature in that area when the effect begins must succeed on a DC13 Strength saving throw or be restrained by entangling vines and roots. A creature restrained by the plants can use its action to make a DC13 Strength (Athletics) check, freeing itself on a successful check. The effect ends after 1 minute or when the assassin vine dies or uses Entangling Vines again.

The vines surrounding the ranger began as non-magical, at which point they were animated by the Assassin Vine's ability. If they are still non-magical, it seems like Wither and Bloom could then have been used to wither them and free the ranger. But if animating them made them magical, Wither and Bloom would not have worked on them.

The Sage Advice Compendium contains the litmus test for whether something is considered magical:

• Is it a magic item?

No.

• Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?

Maybe? What does 'mentioned' mean? Certain the text does not say that the Assassin Vine 'casts the entangle spell'. But does the similarity of the name and the mechanics of the feature resemble Entangle enough to count as it having been 'mentioned'?

• Is it a spell attack?
• Is it fueled by the use of spell slots?

No and No.

• Does its description say it’s magical?

Maybe? The word "magical" does not appear anywhere in the description, but "animates" does. With no 5e definition for what "animates" means, we fall to common English usage – but that includes both the senses of imparting normal and magical movement depending on context.

I note that the Animated Objects described in the Monster Manual:

are crafted with potent magic to follow the commands of their creators…The magic that animates an object is dispelled when the construct drops to 0 hit points

Further, all three of them have:

Antimagic Susceptibility. The armor is incapacitated while in the area of an antimagic field. If targeted by dispel magic, the armor must succeed on a Constitution saving throw against the caster's spell save DC or fall unconscious for 1 minute.

This suggests that "animated" might be a synonym for "magical". Then again, perhaps that only works when creating creatures from objects rather than simply making non-magical plants move.

Are the plants animated by an Assassin Vine considered magical while animated?
Are they subject to withering by Wither and Bloom?