Hi,
The HikaShop recaptcha plugin doesn't interact with the Joomla login. So I'm surprised that this would be the case.
During the login process of Joomla, two triggers are called in the plugins: onUserAuthenticate and onUserLogin
If you look at the code of the HikaShop recaptcha plugin, none of these triggers are present.
And of course, we're not able to reproduce the problem on our end.
I can only think that there is another plugin implementing one of these triggers on your website and that it tries to save the user data for some reason, which then triggers the onBeforeStoreUser trigger which then calls the recaptcha plugin and in that case the recaptcha plugin thinks that there is a new registration going on and checks the captcha solution.
Please try to deactivate the other plugins one by one with the recaptcha plugin to see which one causes the problem. It should be either a plugin of the groups authenticate, user or system.