Cannot index property 'displayName' of type String into type List of Variant

Generally that error means that you are trying to index a field that doesn't exist, so it often occurs when your variable is null or empty for some reason. There are two main ways to address this:

• Determine why your data isn't returning data for those fields (and whether it is valid or not).
• If it's valid that your field may not be present in the JSON result, then use the property or index function to use error handling. Here's an example:

property(
  local!Json.tags,
  "displayName",
  {}
)

Some other general suggestions - the expression that you have provided above is neither valid JSON nor a valid Appian expression, so it may be contributing to why you aren't getting the correct result. Also, I don't see why you actually need to count the display name - couldn't you just count the total number of tags there are?