The thing is, recruiters see gaps everywhere now, so you don't need to make a big deal out of it. The best approach is to be honest but not overly talkative. On LinkedIn, you can simply list your last permanent contract with the end date, and not add a "unemployment" period as such. Gaps are so common that nobody's really going to dig into it unless you put something weird that stands out. If a recruiter asks you about it in an interview, you just tell the truth simply: "I needed time to find the right project" or "I took time to think about my career direction". It's mundane, it's human, and most importantly it's not a red flag.
What really catches a recruiter's attention isn't a period without work, it's a total absence of activity. So use those 6 months to stand out in other ways: a course you took, a personal project, volunteering, anything that shows you kept moving. Add that to your profile, it fills the void and gives context without you having to shout "I was unemployed". And honestly, plenty of candidates go through it. You'll see that in an interview, it's really not the killer question.