If you go there, that's the URL you get. However, if you do anything with the map, your URL changes to something like
https://radar.weather.gov/?settings=v1_eyJhZ2VuZGEiOnsiaWQiO...
Which, if you take the base64 encoded string, strip off the control characters, pad it out to a valid base64 string, you get
"eyJhZ2VuZGEiOnsiaWQiOm51bGwsImNlbnRlciI6Wy0xMTUuOTI1LDM2LjAwNl0sImxvY2F0aW9uIjpudWxsLCJ6b29tIjo2LjM1MzMzMzMzMzMzMzMzMzV9LCJhbmltYXRpbmciOmZhbHNlLCJiYXNlIjoic3RhbmRhcmQiLCJhcnRjYyI6ZmFsc2UsImNvdW50eSI6ZmFsc2UsImN3YSI6ZmFsc2UsInJmYyI6ZmFsc2UsInN0YXRlIjpmYWxzZSwibWVudSI6dHJ1ZSwic2hvcnRGdXNlZE9ubHkiOmZhbHNlLCJvcGFjaXR5Ijp7ImFsZXJ0cyI6MC44LCJsb2NhbCI6MC42LCJsb2NhbFN0YXRpb25zIjowLjgsIm5hdGlvbmFsIjowLjZ9fQ==", which decodes into:
{"agenda":{"id":null,"center":[-115.925,36.006],"location":null,"zoom":6.3533333333333335},"animating":false,"base":"standard","artcc":false,"county":false,"cwa":false,"rfc":false,"state":false,"menu":true,"shortFusedOnly":false,"opacity":{"alerts":0.8,"local":0.6,"localStations":0.8,"national":0.6}}
I only know this because I've spent a ton of time working with the NWS data - I'm founding a company that's working on bringing live local weather news to every community that needs it - https://www.lwnn.news/