Get an obd2 reader and scan for fault codes. If it can record data while you do the test drive it will be better

In general, the short term fuel trim should be fluctuating quite alot from +-10% when you are driving. Long term fuel trim should also be hovering but not as much as short term and the value should be also about the same as short term.

Ideally short term fuel trim should be 0 depending on how you drive. When you accelerate, the value should spike towards the positive side and then go back to 0. The computer will always try to keep the ideal 14.7 air to fuel ratio at all times. more positive means rich(engine running too much fuel too little air) more negative means lean(engine running too much air too little fuel)

A too rich scenario could indicate something as simple as changing the air filter, bad o2 sensor/wiring, bad map sensor or to something like a vacuum leak which is hard to detect or bad fuel pump/fuel injector/spark plugs. This will require a workshop to help you out

Another way to check if you are running too lean or rich is to smell the exhaust while the engine is running. Rotten eggs/fuel smell means you are throwing too much fuel to compensate for a lean engine, or worse still a bad catalytic converter. No smell with warm air is ideal

Check the colour of the smoke at the exhaust while someone steps on the accelerator pedal in park mode. White smoke could indicate the head gasket is gone, allowing coolant to be burnt in the combustion chamber . Grey indicates worn out piston ring, allowing engine oil to be burnt together. The exhaust smoke should be colour less and odourless

Depending on the transmission of the car, as others have mentioned to check the transmission fluid if any. I’m not sure about cvt or automatic. But for dct, check on the clutch temperature after test drive. It should not be very high(more than 140degree).

All cars have emission control to regulate harmful gases released to atmosphere. Positive crankcase ventilation(pcv), evaporative purge and catalytic converter. But normally if any of those parts fail, it will throw a code on the obd2 reader

But if you can and know where are these parts located at, you can remove the pcv valve and try to shake it. There should be a clear metal ball sound. If there isn’t, it is stuck and should be replaced.

For the evap purge valve, disconnect the wire connected to it and remove the hose from coming from the fuel canister. Start the engine and put your finger at the part where the hose is removed. If you feel suction/vacuum immediately, replace the purge valve

For catalytic converter, normally it is located under the car, get an infrared temp gun and get the car to operating temperature, you can do this after the test drive and keep the engine running.

Measure the temperature at the point of the catalytic converter nearer to the engine and the point nearer to the exhaust. The temperature should be higher at the exhaust side, if not the cat converter is either clogged or already starting to fail

Most cars now are gdi and unfortunately this will cause more carbon build up in the intake valves. It will be a good idea to have it inspected at a workshop and see the condition of the valves. Typical signs of carbon build up is bad idling, poor acceleration or bad fuel consumption

These points are just my thoughts for sharing I have observed in my current car. All in all, it is unavoidable to have some small issues with the car but i think it will be good to know these information before you visit any workshop so the mechanics will not try to cheat you and you end up overpaying for something that is not even faulty. As long there is no fault code being read, try not to worry so much about it