What is this half-filled explosion-like icon next to the origin symbol?

This is the Battle-Ready Symbol:

An NPC in the Battle Tower allows the player to give the battle-ready symbol to any of their Pokémon that doesn't already have that symbol or the Galar symbol. The process of doing so also deletes its record of relearnable moves (if any) and replaces its current move set with level-up moves, ensuring that the Pokémon cannot know any moves it could only learn from a previous generation. Beginning with the July 2020 ranking season, Pokémon with this symbol are eligible to participate in ranked ladder and tournament battles as though they were Pokémon that originated in Galar, with the exception of Mythical Pokémon (such as Zeraora) and special Legendary Pokémon (such as Mewtwo).

Essentially, it functions as a symbol showing that the Pokemon is able to participate in official online tournaments.