Flutter still doesn't support liquid glass on iOS so it doesn't seem like a serious contender to me at this point. And due to the nature of how Flutter is implemented, it's going to continuously be an uphill battle. Maybe it's fine if you intend on having a completely custom UI and don't care about platform look and feel.
The new direction isn’t Liquid Glass, but a more unified branding across Android and iOS. WhatsApp, Google Maps, Instagram, Netflix, Prime Video, and many others don’t look dated, because they don’t make heavy use of the older iOS design language at all.
In general, the "render UI as if it were a video game" route feels like a bit of a dead end on mobile to me. On desktop it's more workable but still isn't without issues.