Unarmed strikes are negated by the immunities listed
According to the errata for the monster manual, the immunities in question have been changed from immunity to weapons to immunity to attacks. The exact quote is:
Throughout the book, instances
of “nonmagical weapons” in Damage Resistances/Immunities
entries have been replaced with “nonmagical attacks.”
Note that this had always been the case. Before any errata, unarmed strikes were listed as weapons, and the immunities referenced the weapons. Unarmed strikes were corrected to not be weapons, and the immunities were corrected to reference attacks instead of weapons.
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
Ki-Empowered Strikes aren't magical attacks to begin with!
Ki-Empowered Strikes state this explicitly:
This ability makes the monk's unarmed attacks count as magical only for the explicit purpose of overcoming resistance or immunity to nonmagical attacks and damage. They're not magical attacks as defined by the Monster Manual ("a magical attack is an attack delivered by a spell, a magic item, or another magical source"), and they don't count as magical for any other purpose, such as when considering resistance or immunity to magical attacks and damage, like your monster has. The damage the monk does with their unarmed strike is still mundane bludgeoning damage at the end of the day, it just has this special property that allows it to hurt creatures that would normally be resistant or immune to such things.
Though your monster is immune to damage from magic weapons, that affords it no protection against the blows of a 6th-level monk. In fact, as your monster is both resistant to attacks from nonmagical weapons and separately immune to attacks from magical weapons, as written your player's monk would be able to deal it full damage despite its combination of resistances and immunities, as her strikes will overcome the nonmagical resistance yet do not interact with the magical immunity.
For balance purposes, you may wish to rule (and I probably would rule) that the actual result is that the creature ends up with resistance to the monk's attacks, as if the monk gets to choose the most favourable option between her attacks being considered magical or not; or you could rewrite the monster to be resistant to all physical damage and additionally immune to physical damage from magic weapons, so as to overlap and prevent the monk accidentally loopholing around them.