Unfortunately that’s the point of FreeTube precisely, that’s why it uses libre instances like Piped or Invidious, I think what you mention is impossible.
The closest thing you can use is ReVanced, which is Youtube but without ads, keeping the analytics and recommendations.
Pehaps the user (or in this case the bot) will not go directly to your website, but first to some method of captcha verification or something like that, or like those pages (SteamDB for example) that do not open directly but first open a blank page to verify your network and browser with a captcha.