So, how do I check the appearance tags?

[CourtOfTheGrayWaves]

You know, what the Wiki lists on the TF items pages?

 

[WolframL]

Short of either cracking open a save file (and knowing what the numbers all mean) or using the unofficial save editor, you don't. They're not visible directly in-game though you can infer most of them from how they change the Champ's Appearance description.