No. A "Privatverkauf" is tax free after one year. If you sell before that it is taxed as income.
Crypto is never taxed as capital gains in Germany.
I have to say, this blows the mind for Americans who assume European countries are tax hells. The IRS will tax everything, sometimes before you’ve sold it: I had to pay mark-to-market capital gains tax on unrealized gains in a foreign mutual fund I’d bought before moving to USA.
My humble opinion is that some of this should be harmonized on the EU level. There's no reason to leave so many tax loopholes for those able to exploit them, other than each country's wealthy lobbying to maintain their own peculiar benefits.