Consider a Post-MBA Master's in Business Analytics and Big Data: How Might It Impact My Career Path?

Hi everyone,
I've been a long-time lurker of this forum, and I'm grateful for the valuable insights shared here. I'm nearing the end of my MBA at a Top-10 U.S. program, with graduation set for December. I'm contemplating the idea of continuing my education with a Master's in Business Analytics and Big Data post-MBA. While I am from a U.S. program, I am currently studying abroad at a European institution for my final semester. I came here in hopes of securing an offer in Europe to be near my partner who lives here. Unfortunately, this didn't pan out. I would remain in Europe for this Masters. I'd greatly appreciate your thoughts on whether this decision might impact my job opportunities.

Given the tight job market, pursuing this additional degree might offer me several advantages:

1. Patience for Job Market Improvement: It might allow me to wait for an improved job market in Europe and the U.S. (graduation would be March or September 2025)
2. Technical Upskilling: Pursuing this additional degree could make me more attractive for strategy and operations roles in the tech industry and tech focused consulting teams (think BCG Tech Advantage).

3. Recruiting: It could also open doors for another round of recruiting in tech and consulting, particularly in the European context, if I can establish connections with recruiters and potential industry professionals.

4. Cost: Masters programs in Europe are significantly cheaper. I'm also hopeful that with my background I may be able to get some scholarships.

Fear:
1. Profile: Could this position me as someone who has spent too much time in school and can't cut it in the real world?

2. Regression (no pun intended): My cohort would likely be with students who have minimal or no work experience. In reaching out to one program I was told I am, "overqualified" and should consider Executive Programs. I don't mind if my classmates are younger, but could this impact me wrt recruiting?
   My Background: I have four years of experience in strategy and operations at a Tier-2 consulting firm (think: PwC, BAH, EY). My recent internship was at a Tier-2 strategy firm (think: Strategy&, Parthenon, Monitor). I was working in a niche group focused on PE CDD, which confirmed my interest in strategy work, rather than private equity
   I appreciate any insights or feedback you can provide.