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Typically a miner decides which transactions go inside a block. But does this have to be so? Is the actual mining process just a process to find the right nonce regardless of block contents or does it depend on the included transactions? So: can included transactions be decided after a right nonce has been found?

I was trying to find an article which clearly explains this but obviously I failed.

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Finding a block is, more precisely, organizing a block and finding a nonce.

The miner will work with pending transactions (known) and the miner gets the transaction fees, so the optimal approach is roughly to organize the highest gas consumption and highest gas price, but the miner is not obligated to organize it a certain way.

The block hash includes the hash of the transactions in the block, so yes, the payload matters. No, the transactions cannot be selected after a nonce is found. The hash also includes the hash of the previous block which ensures a continuous ordered sequence of blocks that is easily verifiable.

Hope it helps.

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