Telegram introduces feature to prevent users from texting too often in a group

Wrong, you already do. You either don't realize it, or you're being disingenuous about it.

Did you write 100% of the code of the web browser you used to post your comments?

Did you write the OS that browser runs on?

Did you write the compiler used to build the OS, and did you provably avoid the sorts of issues brought up in "Reflections on Trusting Trust"?

Did you fabricate the chips your OS runs on?

Did you design the die mask for those chips?

Did you build the chip fab facility?

Did you design the locks on the front doors of the chip fab facility?

Did you stay awake 24/7 inside the chip fab facility to make sure no-one broke in to conduct an evil maid attack on the process?

Unless your answer to all of the above is an honest "yes", at some point in the chain of tech, you accepted an outside authority. So kindly knock it off with the "you're automatically wrong because that's appeal to authority!" nonsense.

It's not. If you want to write your own, you have to reverse engineer most of the protocol. The clients aren't fully open source, and when they are, the public code usually lags behind the actual binaries that are released, often by months. It's nearly impossible to write a client that keeps up with the features in Telegram.

You may be thinking of the bot API documentation, which is documented. Many bots don't use that, though, as it's very limiting.

I suspect there is enough implementation there to write a server implementation too, at least a simple one.

The servers behave in very strange, unexpected ways, and the official clients expect these quirks. Most of the third-party clients either use TDLib, which is official and not fully open source, or have also grown to expect these quirks.

Just as a quick example, pretty much everything in Telegram has a numeric ID. Clients, bots, etc. have come to expect that IDs within certain ranges represent certain objects--users have a range, private chats have a range, channels have a range. These ranges aren't documented and may not be obvious even in a fully open source client, but if you don't adhere to them, stuff will break.