In the same app, if you go down Settings -> Advanced -> scroll to the bottom -> Export Telegram data, there is an option to export all chats at once, including some very handy controls like getting only your own messages for large group chats.

ah right, I think that might be what is "Telegram Lite" on the App Store

These are the two options I see to download https://i.ritzastatic.com/static/1e133ef5057a949b7ddd92e5668...

And the 'main' one that I usually use doesn't have export settings that I can find

https://i.ritzastatic.com/static/18db23448a373338766bf419fa0...

I'm not at the desktop right now. Check if the option to do a full (all chats) export still exists.