ArcGIS 10.2.1 comes with 2.7.5, [1] and is very, very old. It was released in Jan 2014 and hit EOL in 2019. [2]
All not-EOL versions of ArcGIS Server support python 3.x. But if you're using ArcMap, upgrading to a later version will not move you to python 3.x: you'll have to migrate to ArcGIS Pro for that. (note for the unaware: this is not a "well just buy the more expensive thing" post. ArcMap and ArcGIS Pro share the same license.) I recommend migrating to Pro for this and other reasons, but I understand that a lot of orgs don't have that on their roadmap.
Out of curiosity, is there a technical reason why your org isn't using a supported version, or is it an "ain't broke" situation? I'd ask migrating to ArcMap to Pro, but if you're on 10.2.1... yeah.
[1] https://support.esri.com/en/technical-article/000013224
[2] https://support.esri.com/en/Products/Desktop/arcgis-desktop/...