Yes, the study published in JAMA Neurology (jamanetwork.com/journals/jamaneurology/article-abstract/2795819) last year really looked at the health benefits. It's very interesting. 9,800 steps a day looked to cut risk of dementia by 50 per cent, which is just huge to me, who has family members with it, but even 3,800 cut it by 25 per cent.
And there was a meta analysis for all cause mortality (www.thelancet.com/journals/lanpub/article/PIIS2468-2667(21)00302-9/fulltext), which show the benefits increasing up to 8,000-10,000 in under 60s and 6,000-8,000 in over 60s.
And another that showed a decrease in risk of all cause mortality of 8-11 per cent per 2,000 step increments (jamanetwork.com/journals/jamainternalmedicine/fullarticle/2796058).
So even if I only get past 3,800 steps (which with a desk job and EDS is a good go some days), I know I am getting a lot of benefits and extra is bonus! Which to me is easier than aiming at 10,000 and getting sad if I "fail".
Back to the original question, 3 km is 4,000 steps for me. I'm 5 ft 7 and have a Suunto watch. My mum has a Fitbit, is about 5,5 and if we do 3 km together, she has almost 5,000 steps. So I think the different watches can give different results too. Others in my family have Fitbits and seem to get more steps than me.