It's unclear what's meant by "private" chats here: I assume Telegram is not planning on breaking the encryption of E2EE Secret Chats and that the non-E2EE Cloud Chats will be subject to greater controls?
1. E2EE is not available on desktop clients at all
2. E2EE must be explicitly enabled for each chat on mobile
E2EE is only as secure as the Ends are.
So, this should demonstrate to you that Telegram private group chats are not E2EE.
Why? Any member of the group can send the messages to the newcomer.
Not that I trust closed and centralized services anyways. But it should be possible.
The typical way group chat encryption is done is the client generate a key per message, it use that key to encrypt the content of that single message.
Then it will encrypt the message key with personal key for each member of the group, and it can only do that for current members of the group.
Once you receive a message the client will use your personal key to decrypt the copy of the message key encrypted with it, then use the message key to decrypt the message.
The problem with this is that, first it does not escale, the larger the group gets the harder it is to encrypt the messages because you need to encrypt the message key with more and more personal keys, this make the work load bigger and the message size bigger as well. Telegram support very large groups that make encrypting groups not practical.
Also Telegram allow you to see older messages sent before you join the group as those get stored in the servers, if you join the group later then for older messages the per message key will not have being encrypted with your personal key so you cannot decrypt it, thus cannot decrypt the message.
You would need to either store the per message key unencrypted in the server and make encryption useless as the server would be able to decrypt it, have the client from some older member of the group re-encrypt the per message key for older messages and send to new members or the simpler approach that Telegram took to not encrypt it at all.
Might as well use Telegram at that point ^_^
that's a feature.
On Matrix it's somehow not a problem.
Telegram allow 200000 members in a chat group.
Signal on the other hand allow only 1000 and ws limit is 1024.
It is possible to have group chat encrypted, but this does not scale very well and allowing new members to see older messages also is trick, although both are possible.
EDIT: i just checked for matrix and while they do not impose an limit their docs do indicate that there are performance problems for very large groups with tens of thousands of members, that while much bigger then signal\ws it is still much smaller compared to telegram.