Q: Skoda/VW Lag on gear shift & RPM going high on accelerating but only partial power transmitted into wheels.

If I understand your narrative correctly, the malfunction occurred exactly coincident to the "service". That raises the possibility of mistakes such as incorrect correct gear (wrong viscosity) or inadequate amount or perhaps components were mistakenly removed and not re-connected (e.g., vacuum lines, sensors). You might re-visit the shop and let them know the problem started the instant you drove off the lot which obviously is quite a coincidence if they had no role in causing the malfunction. Their response to that inquiry will provide a clue: if they are dismissive of your complaint, and reluctant to assist you, that alone would tell me they may have very well caused the problem. Typically, loss of power on acceleration can be due to plugged fuel injectors, faulty oxygen sensors, fuel pump and/or filter, vacuum leaks including that caused by a faulty EGR system, ignition system malfunctions, bad valve timing if the timing belt or chain is worn or skipped, blocked exhaust (e.g., catalytic converter fails or becomes clogged), a faulty airflow sensor or throttle position sensor, and so forth. To pinpoint the exact cause will require an engine loss of power diagnostic. If you request that diagnostic, the certified mechanic will get this resolved for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.