MacBook Pro: administrator password is not accepted?

I have a problem and questions about my MacBook Pro: As far as I know, the password that is used to unlock the laptop is the same, e.g. This is requested if you want to open the lock when editing the "Users & Groups" setting or if you want to install new software. Or am I wrong? Because with this password I can only unlock the laptop and not release new software or open the lock. The guest function is deactivated, which means there's no other user apart from me.
I hope you could understand it, I'm still quite a beginner when it comes to computers. Therefore another picture.

Thank you in advance.

No, that is not what it is called.

The user with whom you log in (let's call him Marie) is not an administrator account.

When setting up the computer for the first time, an administrator user was probably created and then an account "Marie" so that you can log on to the device.

So you have to ask the person who set up the laptop if he can do what you actually wanted to do.

Questions are gladly answered in case of doubt

Should be fine. Are you typing the username correctly? So not the full name, but just the username?

No, not every user is automatically an administrator. I'm assuming that your device has been set up by another user. The first user is usually The administrator.

You are also missing the checkmark for "The user can manage this computer".

Your account or password is therefore not the correct one which is required for the lock.

An existing administrator can also make you an administrator, so that your account is also released for the lock.