ES 300, so its still got a idle air control. It's the squarish passage in the throttle body.
This engine uses a little magnetic drive idle air control valve. When the valve get a little sticky, the mag drive motor doesn't have the ability to move it. Disconnecting the battery when servicing the starter makes the IAC motor drive itself to a factory programed setting it hasn't used in a long time. This is occurred because the the computers learned values has been reset. This previously unused position in the IAC valve is inevitably carbon coated. Now the valve is stuck.
As part of this fix, while you're in there, clean the throttle body. It will help throttle response and is good general maintenance.
Fear not, the fix isn't hard, or expensive.
Take the intake boot off, and out of the way. Below the throttle body you'll see a rectangleish black motor with two screws. Remove the motor, do not loose the small gasket! The screws are tight, don't strip them. Might recommend you break them free with needle nose voice grips.
Once the motor is off, you should now see the brass colored idle air valve drive pin sticking out.
Now, to clean the IAC, You'll need to do this while it's running. Engine won't like to run with the MAF plugged in with the intake off....but, if you unplug the MAF and cycle the key a couple times it will set a maf code, and run on a base tune well enough to get under the hood and manipulate the idle valve and throttle to keep it running while cleaning it.
Locate the idle air port inside the throttle body on the bottom of the throttle bore. Its squarish and before the throttle plate. With engine running, Spray cleaner in pulses, while manipulating the IAC valve in both limits of travel. It should only turn 1/2 to one revolution. You'll be able to keep the engine running easily by moving the valve. You'll feel the stickiness at the limit each way. It will only be slightly sticky by hand..... But remember, the little motor doesnt have much twist, so it doesnt take much.
Don't spray so much or long that you get the cats too hot. You'll be able to tell by smell or visually if they really start to overheat.
Shut it down, disconnect battery and reassemble. By the time you get everything back together you should be able to reconnect battery and it will have cleared all the codes.