In principle, the seller’s German VAT obligation has nothing to do with which eBay site the seller publishes the item.
The seller must register for German VAT as long as it meets any of the following three typical cases:
The company is established in Germany;
Sale of goods stored in Germany;
The sale of goods stored in EU countries to individuals in Germany, and the total turnover of such sales in all channels exceeds EUR 100000 / year.
If the seller meets any of the above conditions, the Seller shall immediately verify that it has fulfilled its German VAT obligations.
If you have further questions, consult your tax advisor or your local tax office in Germany.