I wouldn't be fearful of taking it to a dealer.

As a start, you need to have it scanned for trouble codes. However, I don't know if this can be done at places like Autozone (worth a try). The start-stop trouble codes might be manufacturer-specific and will need to be scanned at the dealership with a Toyota-specific scan tool.

 

Two year old Platinum Highlander with 51K, completely unknown history since you didn't buy it from a Toyota dealer, I assume.

I'd bite the bullet once and go to the Toyota dealer and ask them to scan it, and give you a printed history of the service at Toyota, as a starting point.

Might also check for recalls/service bulletins, get some solid history on it before you go anywhere further.

Might be as simple as needing a new battery, even though your testing shows almost full charge.

 

Here are a couple of web articles explaining the system. Your battery charging messages could be intermittent charging system malfunctions.

Drive Start Control Malfunction Toyota Common Problems

Discover how to address and reset the Toyota Drive Start Control Malfunction Warning with expert insights. Learn how to troubleshoot and resolve this issue, ensuring the safety and efficiency of your Toyota vehicle. Get valuable tips and guidance to tackle this warning with confidence.

www.youcanic.com

What Is Drive Start Control Malfunction?

We saw some complaints on the Internet about the drive start control malfunction. Let’s find out what it is and how to handle it

carfromjapan.com

The dealer is probably better money spent than a independent mechanic who may not have the electronic tools to diagnose this.

 

Another possibility is an electrical problem. Are there any electrical things added that don't look like they're factory? Check for strange wires under the dash or under the hood.
The car may have had (or still has) extra lights, an aftermarket alarm system, or even a GPS tracker for the previous buyer's auto loan.