You also say it doesn't save in incognito but I can't find anything in the source code to support that claim.
I see a bunch of other red flags too, like no obvious monetization, the privacy policy saying updated in 2021, but then a little bit further down it says updated in 2019 (neither makes sense as the domain was registered in 2023), privacy policy sometimes says Nision Research LLC and sometimes Nision Research Kft, the chrome web store page has an email for "gethaystack.com" but the privacy policy says info@browspilot.com (and that gethaystack site has a policy saying "info@localhost"), both of the reviews on the chrome web store are by people clearly affiliated with browspilot, the FAQ says you can't delete things from your history, privacy policy doesn't say where your data gets sent (i see mentions of firestore, firebase in the code, but it does not appear in the privacy policy)
Also this claim on your home page "Your data will only be read and used by you." doesn't align with what your privacy policy says.