Difference between Sign Message and Sign Transaction
Is the difference that for "Sign Message", first a digest is created, which is then signed, while for "Sign Transaction" (in the meaning written above), the input is already a digest, so it shouldn't be hashed again?


No. It has nothing to do with the hashing. Furthermore, the input is not already a digest, it must be hashed before signing. Both the message and the input data are hashed twice with SHA256.

The difference between message signing and transaction input signing is that message signing prepends the string Bitcoin Signed Message:\n (with \n being a newline character, not literally \n) to the message before it is hashed.

Additionally, the 65 byte signature produced by message signing has a byte at the beginning that is not part of the cryptographic signature itself. Instead it is a recovery id so that the correct public key can be recovered from the signature during signed message verification. In transaction signatures, there is a different byte appended to the end of the signature which is the sighash type, usually it is the byte 0x01.