I'm a physics master's student and I will complete my degree by the summer of '22. I'm broadly interested in high energy and condensed matter. One of the profs in my department is offering a project (for the MSc) in high energy that I'm very interested in. He added that he's looking to publish a paper at the end of this project so I will need to commit to doing this throughout the MSc. I've also taken one of his classes so I have some familiarity with him. The project is theoretical and he said it won't involve any kind of computation/data science component. The project is about gravity and information around black hole event horizons.
My question is the following: Suppose I wanted to switch to condensed matter after my masters, would I be at a disadvantage because my MSc project was not in condensed matter? I understand that while applying to grad school in the US, you don't apply to a single prof or a research group, but in Europe you do (?). I'm mainly looking at graduate programs in Europe so that is why I am having trouble with this decision.
Would it help if I have a publication but it is not in condensed matter, as opposed to having done a project in high energy (while applying to condensed matter profs/groups)?
I'm mainly interested in European PhD programs (specifically those in France, UK, Germany, Switzerland, Sweden and Denmark).
Thanks in advance!