Each country will apply its own choice of law rules.
The U.S. rule is that everything other than real estate and business assets not owned by an entity (especially leasehold rights and business licenses), is governed by the law of the place where the decedent was domiciled at death. The main probate proceeding is conducted there.
Real estate and select non-entity owned business assets are handled by a probate proceeding in the state where they are located, which is called an ancillary probate. The ancillary probate proceeding, in general, defers to findings of fact and decent controlled matters (like the content of a will) but matters that a decedent couldn't override by a will would ordinarily be governed by the law where the real estate is located.
If the German asset were located in a U.S. state, an ancillary probate would probably not be necessary and the substance of the distribution would be governed by the place of domicile.
I don't know German probate choice of law rules but the answer from @K-HB suggests that Germany may actually defer to U.S. substantive probate laws in this case.
The easiest solution would probably be to probate all non-German assets in the place of domicile in the U.S. and to probate the German bank account under German succession laws without regard to the U.S. assets, rendering the German proceeding small, simple and plain vanilla. If the account isn't large, imploring people who receive shares under German law contrary to the decedent's intent to make gifts that bring the overall or ultimate aggregate distribution in line with the decedent's intent may be possible, or may just not be worth the trouble to reconcile.
In the U.S., pretty much any probate lawyer will have to do. I happen to do probate law (in Colorado) and have some international experience, but I'm the rare exception in that regard and finding someone with both German and U.S. law knowledge would be very hard and very expensive.
In Germany, this matter would most often by handled by a notary, who in Germany is a legally trained professional with a defined territory sometimes shared with several other notaries in the same district (who buys that franchise from the previous owner) who is a bit of a hybrid between a transactional lawyer acting as a more or less neutral third-party in business deals and other transactions, and a county clerk in the U.S. and the Secretary of State in the U.S. and a probate registrar in U.S. states with the Uniform Probate Code. Unlike a U.S. notary, they don't just verify signatures, they draft documents and maintain public records which are really only quasi-public records. Normally someone more analogous to a U.S. attorney or a British barrister would only be involved in the event of contested litigation over the estate such as a will contest or an allegation of embezzlement by a fiduciary (which is a fight you probably can't afford in an estate like this one even if there are good grounds to litigate one). You would want a notary whose district includes a bank office of the bank where the account is located in Germany.
All European lawyers and notaries are much more familiar with international law than 98% of U.S. lawyers, because international situations naturally come up more often there.