reCaptcha Issues

Hello all
Short introduce of myself.
I am 53 years old, took ownership of a website created and maintained in wordpress. I am an IT System Engineer, so IT is not really far away for me. But i do not have a lot experience with WordPress and so on. But i want to learn.

So here is my problem description and my goal:

I was able today to create a recaptcha for the default contact template and was able to enable it and it has worked. Then i tried the same in wp membership. Installed a plugin Simple Membership Google recaptcha and tried the same for the second plugin for the registration form and password reset form.

However the plugin for the registration form never worked so i decided to delete the keys in google recaptcha and try once again.
Now also the recaptcha in the contact form is no more working. Checking the Webpage with WP it looks ok also the settings looking ok. Checking the contact form on the published webpage it shows: Error for site owner:Invalid Site Key.
I tried to disable, enable again, delete the keys in different ways but i am not able whether to configure it that it works in the contact form for the customer.

So my goal will be to fix as first the contact form and then to set also repatcha for the registration form. This is the bigger pain for me, because this was never set an i have around 20 -30 spam accounts which are trying dailywise to register.

So i appreciate any ideas, help and what will help solve my issues.

I tried with different browsers, clear cookies, private/inkognito Browser and all i know
Unfortunately i dont have an idea, how i can share here screenshots when i dont have pictures stored on a webserver.

Thank you in advance
Regards
J