For any Google Workspace admin, my recommendation is that they actually
disallow the ability to login to secondary accounts, period.
The proper way to use more than one Google account is to use them in separate Chrome profiles, and it's better for everyone if that is the way all users are taught how to do it. Chrome profiles work both on mobiles and computers, so nobody loses anything by doing it the proper way.
And, you as the developer can recommend that in your information wherever you publish your tool.