I run Telegram app on an old IPhone X whose battery is at 76% of “maximum capacity”, as per iOS battery health.
I’m noticing that Telegram app depletes my battery much (ie about 10x) faster than many other apps, such as X/Twitter or even YouTube. I mostly use Telegram to read public news forums, which feature very few videos or images. I did switch “power saving mode” on in Telegram, and that helped only marginally. I don’t feel the difference between Wi-Fi and LTE type of the network connection in this respect.
To reproduce, I recommend getting an iPhone with an old battery, charge it full, disconnect from power socket, and browse through a few channels for 10-20 mins to see battery charge going down fast. Then recharge the phone and play a long YouTube video to confirm that this process is substantially less power hungry.