The delay nobody measures
A buyer who ordered at nine and heard back at six has spent a day not knowing if anything happened. Nothing went wrong, and they will still remember it as slow. That whole impression lives in the gap between the order arriving and you seeing it.
What linking Telegram changes
The order arrives as a message in the app you check anyway, with the items, the buyer and the total. The actions are on the message: accept, mark shipped, cancel. You do not open a dashboard to do the obvious thing.
What the buyer gets in return
A confirmation in the same chat they ordered from. Later, if you add a carrier and a tracking number, the message saying it is on its way, with the tracking visible under the order in the bot.
Each of those removes a question that would otherwise arrive as a message you have to answer by hand.
Why email stays as well
Notifications fail. Phones are left at home, apps get muted, accounts get logged out. Email is the slow channel that does not depend on any of that, so it keeps running underneath rather than being replaced.
Setting it up
Link your Telegram account from the dashboard once. After that every order arrives in both places and you can stop watching one of them. The storefront side is described on Telegram Mini App store; what each plan includes is on Pricing.