I just ran a test on my stock Pixel 8 Pro connected via Proton VPN:
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I opened Firefox and searched DuckDuckGo for "pool heater".
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I scrolled down until I saw an Amazon link, then closed the tab and Firefox.
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I opened the Amazon app. I scrolled through the "deals" on the app's home page and did not see anything pool related at all.
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I typed "pool" into the search slowly, to see if and when "pool heater" was suggested as a search. I typed in "pool" entirely, yet "pool heater" was never suggested.
I don't know what that implies, but it seems like if I am using Firefox, DDG, and Proton VPN, Amazon isn't monitoring my Internet searches.