No, public transportation is not included in the Eurail pass.

Generally speaking, the only local transport included is where rail lines run through the city.

You can’t use most metro/ tram/ buses.

Interrail ist im Prinzip ein ZUGticket.Dajer sind Bus,U-Bahn, sowie Straßenbahn in der Regel nicht enthalten,S-Bahn, Regionalexpress,sowie Regionalbahnen schon.

It’s always difficult to properly answer, if we don’t know where and when you do a transfer by public transport.

Tram/bus/metro tickets are mostly inexpensive. Tickets for transfers in e.g. Paris are best bought at the bar the TGV e.g., to avoid long queues at the vending machines in the arrival station.

In London on the other hand, everything is easily done by contactless payment.