I think exchanges offers better values when it comes to monitoring the price of Bitcoin that's because most exchanges offers you the option of reading the market charts, comparing them to chart history and making good technical decisions. Using telegram to monitor Bitcoin price to me isn't a good option especially when you're a trader. Personally, prefer Bybit because apart from the market charts it offers you, it also notifies you when there's a positive movement in the price of Bitcoin.
BTC liquidity is solid, so the price difference across exchanges usually isn't too significant, I'd say not more than 0.1%. Also, as I mentioned, I'm not an intra-day trader, I hold BTC and ALTs for the long term, so I only need to check the BTC price to understand the market's overall state rather than trying to capitalize on every price swing.
I also use Binance but have the app installed on a separate device dedicated to trading. I use CoinGecko to track my portfolio movements, and I'm also used to CoinMarketcap for getting comprehensive information about any token. However, I frequently work with Telegram for research and teaching, so I also follow crypto news on Telegram and get minute-by-minute BTC price updates through this app whenever I want.