But when it comes to non-legacy addresses there is no standard signature format so electrum generated signatures can't be verified by other wallet software.
I have heard this many times, but I don't agree with it.
In my opinion, it doesn't really matter whether your address is legacy or segwit when signing a message. You sign the message with your private key. Your private key can generate legacy and segwit addresses and your message can be verified using each of them.
All the messages that I signed on all BIP39 wallets are verified on Electrum. The message that I signed on Electrum are verified Bluewallet, Sparrow, Mycelium (a wallet that I am not using). I gard no problem verifying the messages before be it legacy or segwit address.
The people that are having problem are those that are using some online tools to do the verification. It is true that it is private key that is used in the signing and not the address, you are correct in my opinion.