BAS/ESP lights remained illuminated imediately after changing the battery

have vehicle for trouble code

Most of time, whenever battery disconnected, these lights illuminate. A scanner is required to clear and reset. Should this action fail, A code will be set identifying reason

An Electronic Stability Program (ESP)/Brake Assist System (BAS) indicator is standard equipment on all instrument clusters. The ESP/BAS indicator is serviced as a unit with the instrument cluster.
The ESP/BAS indicator gives an indication to the vehicle operator when the Electronic Stability Program (ESP)/Brake Assist System (BAS) has been activated. This indicator is controlled by a transistor on the instrument cluster circuit board based upon cluster programming and electronic messages received by the cluster from the Controller Antilock Brake (CAB) and the Transmission Control Module (TCM) over the Controller Area Network (CAN) data bus.
The ESP/BAS indicator Light Emitting Diode (LED) is completely controlled by the instrument cluster logic circuit, and that logic will only allow this indicator to operate when the instrument cluster receives a battery current input on the fused ignition switch output (run-start) circuit. Therefore, the LED will always be OFF when the ignition switch is in any position except ON or START. The LED only illuminates when it is provided a path to ground by the instrument cluster transistor. The instrument cluster will turn ON the ESP/BAS indicator for the following reasons:

1. Bulb Test- Each time the ignition switch is turned to the ON position the ESP/BAS indicator is illuminated for about four seconds as a bulb test.
2. ESP/BAS Indicator Lamp-On Message- Each time the cluster receives an electronic ESP/BAS indicator lamp-ON message from the CAB indicating that the ESP/BAS system has been activated, the ESP/BAS indicator will be illuminated. The indicator remains illuminated until the cluster receives a lamp-OFF message from the CAB, or until the ignition switch is turned to the OFF position, whichever occurs first.
3. ESP Full Off Textual Message- Each time the cluster receives an electronic ESP Full OFF indicator lamp-ON message from the CAB indicating that the ESP/BAS system has been manually disabled, an ESP OFF textual message will appear within the cluster odometer display. The ESP OFF textual message remains displayed until the cluster receives a lamp-OFF message from the CAB, or until the ignition switch is turned to the OFF position, whichever occurs first.
4. Actuator Test- Each time the cluster is put through the actuator test, the ESP/BAS indicator will be turned ON, then OFF again during the bulb check portion of the test to confirm the functionality of the LED and the cluster control circuitry.

The CAB continually monitors the ESP/BAS circuits and sensors to decide whether the system is in good operating condition and the proper outputs to the components of the system. The CAB then sends the proper lamp-ON or lamp-OFF message to the Electro Mechanical Instrument Cluster (EMIC) (also known as the Cab Compartment Node/CCN).
For proper diagnosis of the ESP/BAS system, the CAB, the TCM, the EMIC, the CAN data bus or the electronic communication related to the ESP/BAS indicator operation a diagnostic scan tool is required. Refer to the appropriate diagnostic information.

The ESP and BAS warning lights may illuminate due to a failed brake light switch. Replacement of the failed switch should correct this concern. A recall on certain 2000-2002 models have been recalled for a related issue

Doesn't seen like anything, until you road test with
scan tool & look at data

Maybe a wheel sensor issue.
Charge battery fully - an under performing battery can create gremlins.

un hook your battery to reset the computer , if it persits you may have to change the esp sensor keep in mind once you disconnect the battery it will clear your error codes and it can not be read later.

It look like your ECU does not recognize the throttle body. Reasons being removal of battery for a long time. Try doing an adaption and also run a Diagnostics for other issues

ESP = Electronic Stability Program
BAS = Brake Assist System

you need to see what the eng lite for if there is a trans codes usually the pcm wont let the speed go over 40 stays in safe mode untill you fix the problem or change the sensor,for the esp you need to chage the esp sensor and recalibrate by the dealer