Took the engine to a machine shop friends recommended me.
They checked everything and said it's no problem to get everything fixed, they even gave me quite good price for everything.
They gonna enlargen the cylinders to 1. OS and the crankshaft will be lapped to 1. US.

However, I now ran into problems sourcing the original 1.OS pistons for the last production year EJ20R.
My Subaru dealer first said it would be no problem to order them, but now that he did, Subaru Japan said the pistons would be out of stock.
I now placed an inquiry at amayama.co.jp in hope that they may know a different source, waiting for them to reply now.

If that doesn't work out:
Would it be possible to use the pistons from a pre 31.07.1997 production EJ20R or an EJ208?
These pistons still seem to be available, even here in Germany.

...or could I run a BH5 TT engine (EJ208) with the ECU of my BG5 TT, as in just using the block and cylinder heads from the BH5 TT?
BH5 engines seem to be quite easier to source than a BG5 TT.