Product design to product management

Personally think it will only add to it.

PMs are considered more business, strategy, data and project aware.

Use this to position yourself as a much smarter and dependable designer for your next stint.

Also, PMs get paid more. Consider switching tracks if you like it imo.

No it will not. You'll be in the company for way more than 3 months right - focus on that while putting the experience in your resume/interviewing later.