Well, here are my 2 cents. If you want the advice of a real tax lawyer, you have to cough up more (edit: to pay somebody else).
I assume you are under the normal taxe regime, neither at source (Quellensteuer) nor in another special tax situation.
For the administration of your securities by third persons, securities held in your private property, you obviously just have this flat rate of between 0.3 and 0.5% up to a certain limit (5k?). After that and according to a newer court decision, you have to itemize. If the deductible costs are not well enough separated by the financial institutions, we can forget it.
The fact that you pay your own GmbH to do this does not change the deductions for you. It just creates administrative hassels with the taxation of the Gmbh, the books, the taxes and social security paymens on wages etc.
So what if you put your securities into the GmbH? Then you have still the described hassle, but you can deduct all expenses from earnings. Unfortunately, capital gains become taxable in a company. And all gains that you receive from the company will be taxed again (maybe as privileged dividends) in your declaration.
Let’s assume you wanted to deploy some capital for risky crowdlending at higher rates. There, the company would allow you to compensate losses from one credit with gains from another. And credit income is taxable anyway. Plus you could pay certain expenses at least partially over the company(phone/compuyer). It could make sense.
This is what I know.