Off-the-cuff prediction: there probably won't be one dominant search engine after Google stumbles, for a few reasons:
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All of them are making the exact same mistakes as Google, as self noted (when they aren't having their own unique dumpster fires)
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AI has made it much easier to spam searches with SEO shite, so any attempts at algorithmic search risk being spammed to death in short order
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Public trust in tech is utterly shot to hell - not sure how much people trust search specifically, but I suspect people are currently trusting word-of-mouth (e.g. Reddit, TikTok) over whatever any of the major search engines are providing right now