Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
If the label you designed is the same size as the Avery label then you can just copy it and paste it on the Avery label template.
If it is different size you could save the original design as a picture (I prefer PNG) and then insert it on the Avery label, resizing the picture to fit. You cannot just take a combination of text boxes and pictures and other elements that are part of your custom label design and just scale all those elements to fit at one time...unless you convert to a picture first.
Probably the best approach is to simply rebuild the custom label on the Avery template.
Once you have the Avery label template created you just print multiple copies of the single label. Based on the Avery label chosen, Publisher will know how many copies to print for sheet of those specific labels.
Here is a link to to several articles about creating and printing labels including mail merge for further study: https://support.microsoft.com/search/results?query=labels+Publisher&isEnrichedQuery=true&src=as
DavidF