signrawtransactionwithwallet seems to break the existing signatures of some of the inputs

Start by reproducing the issue with the supplied before-and-after raw transactions and the signrawtransactionwithwallet RPC, then inspect how already-signed inputs are handled when another input is signed. Done means existing valid scriptSigs remain unchanged and the RPC no longer reports invalid stack size for those inputs.

It seems that this rpc alters the scriptSig of all of the inputs that were already signed (second and third vins in this case), except for the first one.
This is an example with 4 inputs, where the first 3 are transactions that are already signed:

Before executing signrawtransactionwithwallet, I have this transaction:

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

and after executing it, I get this one:

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

By decoding both, it seems that this RPC alters the scriptSig of all of the inputs that were already signed, except for the first one.

The error that is returned by the RPC on the inputs that were already signed (second and third vins in this case) is:
"Unable to sign input, invalid stack size (possibly missing key)"