Invest in Vanguard Index Funds (from Germany)

Curious to know why is that?

Generally each region in the world has it's own regulations and specific financial products. The VTSAX is an American product. You also can't buy it in Australia or even in Canada.

So to a large extent it really boils down to regulations. German (or generally EU) brokers are only allowed to offer UCITS regulated funds to their retail customers. Furthermore the EU Directive 2014/65/EU massively restricted the investable universe for retail customers in the name of consumer protection.

You may bypass this regulations by becoming a customer of an international broker, but the really serious downside with that route as a German citizen (which you are?) lies in complicating your tax return. While german brokers handle all tax issues and withhold the appropiate amounts for their retail customers directly, as a customer of an international broker you must handle the tax completely yourself.

eToro is one of those international brokers, quoting from their help page "Do I need to pay taxes on my trades?"

It is our clients’ responsibility to calculate and pay any applicable taxes in their country or countries of tax residence.

Especially with funds, that really is a can of worms, which I wouldn't advise you to open. Just in 2018 Germany passed a law (InvStG), which massively complicates the tax handling of accumulating investment funds. That's really no fun to do by yourself. :-)

How about a reliable broker that offers most of Vanguard Index Funds to be traded within Germany?

The international divisions of Vanguard decide by themself, which funds are interesting for their local markets. Instead of searching a different broker, you may be better of finding alternative funds:

• Maybe use the Vanguard FTSE All-World UCITS ETF (USD) Accumulating instead of VTSAX?
• Have a look at the iShares S&P 500 Information Technology Sector UCITS ETF USD (Acc) as replacement for the VGT?

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On a general note:

If I recall correctly the international Vanguard divisions are for profit organizations and not organized in the same way as in the US, were the fund shareholders are the owners of Vanguard (making it work like some kind of cooperative, which makes Vanguard so special in the US market).

It somewhat has a downside, if you get all your financial literacy from US books/online forums, while not being located in the US. Literally all the products that get talked about aren't available to you, also a lot of the concepts (especially in regards to retirement strategies) don't apply to you, as the tax regime is totally different.