Need to provide a phone number to Apple review to login into the App

Usually every user has their own phone number that they will use.

But I need to provide one to Apple so that they can check my app.

That is the same as your trusted phone number.

Then you need to -> Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com

• and edit / update your trusted phone number.

Get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK) 

see -> Germany

or call direct to -> 0800 6645 451

But what's with the OTP?

See -> Automatically fill in SMS passcodes on iPhone

Automatically fill in SMS passcodes on iPhone – Apple Support (UK)

• When you sign in to some apps and websites, a one-time SMS passcode is sent to your iPhone. As a security measure, you are required to enter the code into the app or website. iPhone can detect the passcode in Messages and display it above the keyboard.

Get a verification code and sign in with two-factor authentication

Get a verification code and sign in with two-factor authentication - Apple Support

How do I give the Apple reviewers access to that?

Do I just go to a shop and get a SIM card?

It will be send to this number and not to theirs.

Yes, you need to have a SIM card, look for / visit a carrier, take a subscription, postpaid or prepaid card.

Check whether the SIM card is suitable for your iPhone.

Then you need to -> Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com

• and edit / update your trusted phone number.