No, it is not magical
Jeremy Crawford clarified this point on Twitter, using Sage Advice to support it. It is "background magic" similar to the breath weapon of a dragon.
Grant Myers @realgrantmyers
@JeremyECrawford ki is described as magical, but nothing in stunning strike says that it's magical. Can you confirm that it is not please?
Jeremy Crawford @JeremyECrawford
Neither the Ki feature nor the Stunning Strike feature (PH, 78 & 79) is defined as magical for game purposes. #DnD
Joe Lastowski @JoeLastowski
Replying to @JeremyECrawford
Except in the section called "The Magic of Ki" at the start of the Monk description.
Jeremy Crawford @JeremyECrawford
That is an example of the background magic I talked about in Sage Advice. Look for "Is the breath weapon of a dragon magical?"
Therefore, just as a dragon's breath weapon is not considered magical, a monk's ki is also not considered magical. They all work in an antimagic field.
However, Ki-Empowered Strikes are specifically magical
The feature says:
Starting at 6th level, your unarmed strikes count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
This is also supported by Jeremy Crawford's tweet.
Jeremy Crawford @JeremyECrawford
The Ki-Empowered Strikes feature says a monk's unarmed strikes count as magical. That magic is suppressed in an antimagic field. #DnD
With your houserule, the DPR is huge
Natural Weapons are not Unarmed Strikes, making them so is a very unofficial, very unbalanced houserule.
Level selection
The best damage available in beast form is 24(4d8+6, Triceratops Gore) at +9 to hit, but you need 15 levels of Druid for it. To get the Extra Attack, you have to have 5 levels of Monk.
This is all of your 20 levels.
Starting Ability scores
for Human Variant with the Resilient(Con) for Concentration:
Str: 8
Dex: 16
Con: 14
Int: 10
Wis: 16
Cha: 10
ASI Monk 4: Sentinel, for out of turn DPR
ASI Druid 4: +2 Wis, for AC
ASI Druid 8: +2 Dex, for Flurry of Blows
ASI Druid 12: +2 Dex
Calculation
Assume AC 20 for the enemy, it is not unreasonable on level 20.
Official DPR:
+9 to hit, 2 x 24 (Gore) = 0.5 x 2 x 24 = 24
+11 to hit, 2 x (3.5+5) (Flurry of Blows) = 0.6 x 2 x 3.5 = 10.2
Alltoghether it is 34.2 vs AC20.
This is a very sudden jump however, at level 19 you either do not have Triceratops, or Extra Attack. Without Extra Attack you do 12 + 10.2 DPR, below a 17th level Monk.
Houserule DPR:
+9 to hit, 2 x 24 (Gore) = 0.5 x 2 x 24 = 24
+9 to hit, 2 x 24 (Gore as FoB) = 0.5 x 2 x 24 = 24
Alltoghether it is 48 vs AC20.
Extra Attack makes a much smaller difference now, as the FoB does the same damage as attacks done with your action. This is very unbalanced.
Compare it to 17 levels of Monk:
+11 to hit, 2 x (1d10+5) (basic attack) = 0.6 x 2 x 10.5 = 12.6
+11 to hit, 2 x (1d10+5) (Flurry of Blows) = 0.6 x 2 x 10.5 = 12.6
This all remains the same in the next 3 levels; 25.2 vs AC20.
Best Answer
A bear's Bite or Claws attacks are considered natural weapons
Looking at the basic rules for monsters' actions, it says this about their attacks:
So it seems as though a bear's Bite of Claws attack would be considered natural weapons.
From the basic rules section on combat, melee attacks specifically, it includes the following:
It appears that an unarmed strike cannot be a weapon, and a bear's Bite and Claws attacks are considered "natural weapons", so RAW, the monk's Ki Empowered Strikes would not be applicable to the bear's attacks.
Unofficial rulings (taken from this answer)
There is no official ruling on this issue given in the Sage Advice Compendium as of 2019. Unofficially, rules designer Jeremy Crawford has clearly stated many times on Twitter that natural weapons aren't used for unarmed strikes by default.
For instance, in this tweet:
A second user interjected, and Crawford responded:
Crawford reiterated this again a few years later:
And again:
He has consistently stated that attacks with natural weapons are not unarmed strikes, except where the rules clearly state an exception. This is consistent with the rules references above.
Related answers: