Register form, V2 checkbox only shows once you click submit button

This is indeed how the module works, for both types of recpatcha ( v2 and v3 invisible ) all recaptcha related javascript calls are being triggered only after submitting the form. The main reasons for that are following:
1) when developing the module, there was a lot of rumors saying that recaptcha might become a paid service, so by doing API calls only when it's really needed we've limited the total amount of calls, this also has good performance impact (imagine having a simple newsletter form added to footer on each page and making recaptcha calls everytime the page is loaded vs making that calls only when user interacts with form )
2) most of recaptcha logic is delegated to JS libraries, which makes it easier to work with different caching systems

Aha, thank you for the info!