So funny to hear this. 3 month notice periods (in either direction) are bog standard in parts of Europe. And it's entirely normal to just keep working, training your replacement/finishing off stuff.
That's my point about it being funny. In one place a 3 month notice period is considered a gardening leave for special higher level employees and you still basically get escorted out of the building.
In other parts of the world it is just the bog standard notice period and nobody is escorted out of any building and expected to keep working during that 3 month period.