I want to point out that E2E encryption on Web doesn't make your conversation more secure than regular HTTPS encryption without E2E encryption. The core to the argument here is the threat model. The whole point of using E2E on any conversation is to make sure that even the service provider cannot read your conversation. It's very clear that the threat model is againsting the service provider. However, the very same service provider of your conversation channel also provides the underlying encryption application on Web. That means, if the service provider wants to act evil, it's always possible to sneak you an application that steals your conversation by simply not applying E2E encryption, or just eavesdropping before encrypting.

The root of the problem is that Web application doesn't have a root of trust. As long as this problem is not addressed, E2E encryption on Web will always be meaningless.