So does Android OS provide auto switching to 3G/4G/Prefer LTE mode when network turns on and auto switching to 2G mode when I turn off the mobile data?
No, it doesn't
If there is no such option, how can I send this as a suggestion to Google or Android developers?
Yes. You can, as mentioned here
You can help improve Android by reporting issues and feature requests in the Android Issue Tracker.
IMO, this would fall in the Networking section.
I wouldn't cross my fingers hoping something will come out of the bug report but it's your call.
If you root your device and install Xposed framework, you can install Gravity Box and select Smart Radio option (Note: As of today, Xposed framework has not been ported to Pie; Gravity Box module & Xposed framework vary as per Android version). Also, Gravity Box works best on AOSP ROMs so it's better to check out in your device forums if it works well or not.
Using this feature you can switch to 2G when you are not using the data network and switch to selected network automatically when using data. I use it and snapshots below show the choices of network when
connected / not connected to data (power saving and normal mode). In addition you can fine tune switching and create a Quick Settings tile for it.
(Tap to enlarge)