Toyota complained about poor performance on all of Unity, UE and Godot, but also about long startup times with Godot.
I don't know how bloated Godot is, but AFAIK libgodot development started as part of Migeran's automotive AR HUD prototype so I'm surprised to hear it has poor startup time for a car.
Godot is pretty lightweight (especially considering how powerful it is), generally about a second or less. But maybe they are looking for a fast enough startup time that the engine can be started when showing something onscreen and torn down when not visible. In which case, I can see the startup time being an issue.
The fact that they tried other engines seems to imply that non Flutter options were... Options.
If literally the only option was an embedded flutter view, then there was never more than one viable solution and looking into unity etc was wasted effort.
It’s possible to integrate other things into Flutter.
However, it’s not easy. I think their options were either a popular mainstream library or a custom solution, not investing into something more obscure and less popular.
They already tried other engines, such as Unity. The team didn't just go off and build something without trying existing solutions first.