Hello Elias!
Yes, the muggle war is completely done with. The wizards of the UK aren't quite as aligned with the muggles as the Hexenreich was with Nazi Germany, so the Muggles of the UK aren't aware of what's going on with Wizarding UK.
The takeover of Hexenreich was completely separate from anything Nazi Germany had going on. They have power and threats, and a general lack of remorse for what they're doing. There is a resistance faction, and they're doing their work, but they are receiving no help from outside Wizarding Britain.
I hope this answers your question, if not feel free to respond and ask.