Not so long ago connecting your iPhone to Bluetooth devices was a real problem for the neck. Control Center's AirPlay button made it easy to connect to specific devices, but with iOS 13, Apple was able to dramatically improve the connection to wireless devices such as AirPods, speakers, and keyboards.
If your iPhone is running iOS 13 or later, unlock this feature Go to the Control Center, and then touch either 3D or long press the connectivity panel in the upper-left corner to see more options. Next, make sure Bluetooth is turned on (so that the speech bubble is blue), and then touch 3D, or long press the speech bubble. See a complete list of all previously connected Bluetooth devices without opening the Settings app.
This greatly facilitates reconnecting to a previously paired Bluetooth device. Especially useful if you frequently switch between devices, eg. For example, a home speaker, your car stereo, and your AirPods at work.
If you need to connect to a new Bluetooth device, it will not appear on this list. Fortunately, at the bottom of the list, Apple added "Bluetooth Settings", which gives you instant Bluetooth settings that allow you to connect to any device.