phpBB up to and including 3.2.5 does not support reCAPTCHA v3, released by Google in October 2018.
The Google-provided reCAPTCHA PHP client (https://github.com/google/recaptcha) as part of phpBB is currently the 1.1.2 September 2015 release, and would need to be updated to the current version which support both reCAPTCHA v2 and reCAPTCHA v3.
Presumably it then needs to be decided whether phpBB itself intends to support both reCAPTCHA v2 and reCAPTCHA v3, or to continue with the "only support one version at a time" approach which appears to have been used up until now.
Whatever is decided for the "reCAPTCHA v2 and/or v3 supported" question then determines what kinds of changes need to be made to the phpBB reCAPTCHA plug-in itself, as well as to the proSilver template for reCAPTCHA.
Currently the phpBB reCAPTCHA plug-in configuration page and documentation is not specific on whether "only v2" is supported, and users are entering in Google reCAPTCHA v3 API keys without expectation of whether they should or will work. The <div> tag approach phpBB currently uses for specifying the API key is not compatible with reCAPTCHA v3, so the manner in which phpBB tries to invoke reCAPTCHA when the user has entered a v3 API key causes an "invalid API key" error to be shown.