Ummm.....
We use the standard way to "flag" a message, it's in the IMAP spec since 2003.
How a mail service or another mail app interprets that - is out of our control.
Turns out, Gmail has a special folder that contains all starred messages. Other mail services don't.
If Inbox app has a way to "pin" a message - well good for that app if that's how it interprets "starred" or maybe it's a whole separate feature, but again I don't think this is something we can access.