if I’m using an open source GPL-3.0 library in my saas product, do I need to publish my code under the same license as well?
If you only run the software on servers that you control, then that is not considered distribution according to the GPL license and thus you are not required to publish your source code.
If you give the binaries to others to run on their servers, then you are distributing the software and you need to observe the restrictions of the GPL license. That means that you must also provide your source code under a GPL-compatible license.
By law you are free to license your code as you decide to license it. No one can force you to do anything. Just be prepared to fight for your right in a court in case some FSF, FSC or some similar organisation is going to bully you.
So instead ask yourself: do you have the resources to go to court? Are you a sort of person who gets easily intimidated by threats and false claims? You can estimate your risks by counting all the down-votes this answer gets from the fascists around here alone.