Yes - Wise absolutely will do the trick.
You’ll have a Euro bank account with an “IBAN” (which is the pan-European bank/account information, that is used by many other nations outside Europe).
But, your account will also be “reachable” from/to the U.S. using the local ACH system (ABA routing code and checking account number). So you’ll be able to use your funds to make payments on either continent, as well as deposit/withdraw money in either.
Finally, yes, you can get a EURO debit card from Wise to withdraw cash from ATMs. In Germany, credit cards are fine to use, but cashless purchases are very popular, specially the younger generations.
Been using Wise on a very regular basis for ages, for personal and business use (and also to have access to the GBP realm.)