Can all messengers with "E2E" except jabber read your messages?

Question

Encryption

End-to-end encryption is when "regardless of the server" keys are generated in clients that encrypt correspondence.
But how can you be sure that if "correspondence with Vasya encrypted with his key" falls into the client, then this is REALLY the key generated by Vasya?

Keys must be exchanged without passing the server, for example, by email or in person, or the server can do mitm and read your correspondence, am I right?

Answer 1

Yes you are right -

Keys must be exchanged without passing the server, for example, by email or in person, or the server can do mitm and read your correspondence

Answer 2

Keys must be exchanged without the server, for example, by email or in person, or the server can do mitm and read your correspondence, am I right?

Undoubtedly right. When I read on whatsapp that the correspondence "will not be available to anyone", I always laugh. "No one but whatsapp admins, of course" :)
Example.
An office where correspondence is encrypted with certificates. AES256, everything is grown-up. Who, besides the sender and recipient, can read the letter? That's right, the person who generated the certificate :D