Vlad As a direct competitor to Google, your basic value proposition is that you're an alternative to Google while delivering comparable quality of search experience. Of course, Kagi has many features that Google can't or won't support, but not being involved with Google's ecosystem is a large draw for your customer, especially this early in the adoption curve where a large chunk of your users are early adopters and enthusiasts.
I am cognisant of the fact that you cannot develop a custom experience for something like forms when this is a solved problem, but there are many third-party SaaS or self-hosted solutions that should be trivial for you to spin up. For example, Yakforms is GPLv2 and actively maintained, but there are many others.
I'm not even asking you to go back and rip up this existing interest form, since doing so would be a waste of time that's better spend improving the core product. But please consider these issues when you're putting together the next 'expression of interest' form.