Why are my Pokémon dozing off?

This has to do with the Pokémon’s Affection. While the source has not updated to reflect Sword/Shield yet, this dialog also appears in Sun and Moon in the same scenarios.

The dialog you see is just alternate text when your Pokémon is thrown in at the beginning of the battle, and it is varies based on the Pokémon’s affection. Based on the information in your question (and comments), the affection level is 2 out of 5.

In Sword/Shield, you can check your Pokémon’s affection by playing with them in the camp. Simply call your Pokémon over and talk to them. When you talk to them, the number of hearts that are shown above their head indicates the affection level.

According to Bulbapedia, the following are benefits your Pokémon will get based on it's affection level

• At affection level 2 and higher, a Pokémon will gain 1.2 times the normal experience from battles.
• At affection level 3 and higher, a Pokémon may endure attacks that could otherwise make it faint and survive with 1 HP (including confusion damage). This can activate multiple times per turn.

• At affection level 4 and higher, a Pokémon can sometimes:

  • Avoid attacks, even when they have 100% accuracy. This can activate multiple times per turn.
  • Shake off status conditions at the end of the turn.
• At affection level 5 and higher, a Pokémon's chance of scoring a critical hit is doubled.