I am seeing a lot of people signing messages with Segwit Address (starting with 3 or b).

There is no standard to verify these addresses.

Electrum is somehow verifying them, but only Electrum, and it's nonstandard.

In future there will a standard for those address, to be verified in any wallet, and not necessarily the same Electrum did. In future those signed messages may not be able to be verified. I think it's better to sign with a legacy address for now.