How do undergraduate theses affect master's application?
It has, typically, no harmful effect.

In most cases, you will declare the title of the thesis within your CV, or upon request of either potential supervisor or admission committee. Furthermore, as your current advisor would, supposedly, be among your referenvces, she might talk about it within addressing your applied effort onto the thesis progression, probablely.

As you notice, required pointers to the thesis will be taken into account, even without its completion, within your application.

Good luck