This is also frustrating for our team. I would actually prefer being able to specify which team I want to go to in the URL (like we are allowed to do for the developer portal).
If there was even a hacky way to set the value at the key "sessionToken": at the endpoint https://itunesconnect.apple.com/WebObjects/iTunesConnect.woa/ra/user/detail I'd be satisfied with that.
It just gets really tough to always have to look up my clients Legal organization name in our CRM since Apple Developer uses Dunn & Bradstreet which uses their state filings (which for some states uses handwritten, error prone forms that swap words). It'd be really nice if I could use our client database to just always visit the right page on App Store Connect.