I've tried the same and don't find the results super similar. Both search engines seem to think that you're trying to repair the old tire. However the second Google result is goodyear.com which, while trying to sell you tires, does explain how to use the spare:
On Kagi you have to go until the 10th result to get something from Bridgestone, which explains the same thing while being less aggressive about selling tires:
https://www.goodyear.com/en-US/learn/tire-care-maintenance/h...
On Kagi you have to go until the 10th result to get something from Bridgestone, which explains the same thing while being less aggressive about selling tires:
https://www.bridgestonetire.com/learn/maintenance/how-to-cha...
So the trade-off seems to happen between seeing fewer ads and having better tolerance for imprecise queries.