Is a separate garage cheaper?

That also depends on what the property allows. It's not possible on every property, and on some properties the garage right next to the house is perfect. I wouldn't generalize that.

Yes, you just have to be aware of what kind of building structures result and how quickly things are placed there that perhaps shouldn’t be placed like that. A double garage with space for drinks, tools, bikes is quickly 8x8m in external dimensions. Adding that to a 10x10m house creates a building with 18m width across the property. When considering this, you should also not forget the issue of access. This is rather unproblematic, for example, if the street is to the north and you want the garden in the south. House 3m away from the street, garage set 2m further back and flush with the house towards the garden. That gives a consistent concept, closed to the street and economical with the property. The opposite is rather bad. I see 20m long driveways to a garage at the far end as a sign of poor use of the property.

I am always in favor of giving every thing its place and not planning crutches from the outset. What am I supposed to do with the drinks in the garage at -20 degrees in winter? And won’t the tools rust there? Or was it about garden tools? For that, a wooden shed costing a tenth of the money is sufficient, I think. Do you really want to have a (men’s) kitchen next to the exhaust fumes and tire dirt? Anything directly attached to the house takes away your opportunity for windows. The expensive room is devalued because no natural light comes in. The larger the property and the budget, the more likely you are to build free-standing.

A garage should always be well insulated and also able to be heated. And indeed, my barn is the nicest place for me. You can make it very cozy.

A garage should always be well insulated and also be capable of being heated.

You are confusing something. What you are describing is the house. ;)

And don't the tools rust there?

As long as you don't turn your garage into a dripstone cave, it's not a problem. I would definitely store batteries indoors in winter because of the cold. A drill with a plug is unproblematic though.

So, our garage is not heated now, but it is definitely insulated. And we haven't had any subzero temperatures in the garage in the last 7 years. But we have also rarely had them outside in recent years. In any case, no drinks have frozen here yet. In winter, you at most save on the refrigerator. And the tools haven't rusted either. Tool batteries as well as the batteries from the e-bikes have been stored in the garage for years. I wouldn't know why I should bring them inside now.