No. You cannot work part-time or do an internship in the UK with a UK ETA.
A UK ETA is used for limited short-visit purposes such as tourism, visiting family, short business trips, or transit. It cannot be used for employment or work-related purposes.
Therefore, if your purpose of visiting the UK is part-time work, an internship, or employment, you cannot enter the UK with a UK ETA for that purpose.
Before preparing your trip to the UK, check your purpose of visit first. If your visit is for a permitted short-term purpose, apply for your UK ETA before departure.