While version 1.1.1 was purely for stability, the "good story" elements you are looking for were added in subsequent major updates:
The for the Nintendo Switch, released on December 2, 2022, was a minor technical patch. It did not include new story content, which instead arrived later through free content waves in 2023. Update 1.1.1 Key Fixes Sonic Frontiers Switch NSP/XCI Update 1.1.1 ...
: It resolved an issue where the Kronos Island Titan boss (Giganto) would sometimes disappear after a player reattempted the fight. While version 1