Update: This is now accessible in-game since the 1.2.1.3 patch!
Under the "Pokémon" menu, you can check under the Pokémon name in the left side:


You're right: the game doesn't provide this information in an accessible spot.
As far as I know, the only way to test this is by playing in Practice Mode, and comparing the damage inflicted to the clone with / without some equipped items.
People have already done the hard work for us, so I'll just quote Serebii here:
Pokémon |
Attack Type |
Venusaur |
Special |
Charizard |
Physical |
Blastoise |
Special |
Pikachu |
Special |
Alolan Ninetales |
Special |
Wigglytuff |
Special |
Machamp |
Physical |
Slowbro |
Special |
Gengar |
Special |
Mr. Mime |
Special |
Snorlax |
Physical |
Blissey |
Special |
Gardevoir |
Special |
Absol |
Physical |
Garchomp |
Physical |
Lucario |
Physical |
Mamoswine |
Physical |
Crustle |
Physical |
Greninja |
Physical |
Talonflame |
Physical |
Sylveon |
Special |
Zeraora |
Physical |
Cinderace |
Physical |
Greedent |
Physical |
Eldegoss |
Special |
Cramorant |
Special |
Note that the basic attack of each Pokémon might use a different attack type than listed.