Hi @hatelenovoyoga,
Have you tried using a different, known working compatible charger to see if the laptop started to charge when it is connected, you didn't say?
Try using a strong light and a magnifying glass to visually inspect the USB-C charge port pin connectors (where the charger plugs in) to make sure that they're all there and not that some may be bent, broken or even missing.
Here's a [https://www.allaboutcircuits.com/technical-articles/introduction-to-usb-type-c-which-pins-power-delivery-data-transfer/|link] that describes the USB-C pin functions that may help.
''If there are missing, bent pins etc'' then the [https://www.amazon.com/ZAHARA-Charging-Connector-Replacement-920-13IKB/dp/B0B5DMN6GH|charge port] (supplier example only) will have to be replaced. You will need smd soldering skills and tools to do the repair. Here's the [https://download.lenovo.com/consumer/mobiles_pub/yoga920-13ikb_yoga920-13ikbglass_hmm_201709.pdf|hardware maintenance manual] that may also help as the systemboard will have to be removed so that the port can be replaced. The manual details how to do this.
''If the charge port appears to be OK,'' here's a link to the [https://www.alisaler.com/lenovo-yoga-920-lcfc-nm-b291-rev1-0-schematic/|schematic] for the systemboard (if your model is an NM-B291 REV:1.0 that is). Go to p.41 to view the connections for the charge port so that you can check if power is getting through the port OK and how far into the board it gets etc.
Hopefully a start.