NAMD

Here is another mathematic constant for you, dear readers: Turrini-Zinzi-Belinchon's normalized angular momentum deficit (2020). This takes a solar-system for which we may account for every planet in it: semimajors and masses - only (for now). We calculate that ideal's whole angular momentum. Then we consider the eccentricities and inclinations and run the calculations again. The eccentricity and inclination, which we'll remember from Kozai von Zeipel oscillate, turn out to lower the momentum of the total. Therefore the deficit reflects how messy the system.

This works for systems where we own those statistics, of course.

Mostly they'll be transits such that multiple planets here will not be mutually inclined. Those will be tight orbits. Einstein starts wrangling Newton for Mercury's orbit. Further-in, tides should be raised on the star, which where eccentric Kepler teaches to undercut the planet's momentum from ideal i.e. increase the deficit. If the planets be resonant, their mutual planetary (and, internally, tidal) interactions are non-Keplerian; making "eccentricity" into a moving target. Rather, we see from the Jovian system that a resonant system should lose energy: here through Io, literally disintegrating over time and radiating heat.

On the high end, sometimes - for systems closer to ours, or very young - we can image the planets directly. Or, the dynamics have been studied to stick some constraints upon eccentricity and inclination both. Which together lower a ceiling upon momentum.

Their map marks our system's NAMD to two thousandths: 0.002, or 2 x 10^-3. "Thanks" to Velikovsky, others have done enough dynamics to declare this as longterm stable, although we'll not live to see what Gliese 710 shall do unto us.

Turrini, Zinzi and more - Polychroni and Danielski were media-available - have posted a followup from their model. Evan Gough (h/t toughsf) summarises: 0.002 is a mean and median for sub-G stars with their outermost planet ("Pout") rolling around in less than a Venereal year. Our system's longest year, for such as matter, is Neptune's at 1.648 x 10² years.

"Pout" year, NAMD, and stellar-mass all correlate at heavier G on-up. Pout and starmass should indeed correlate - with age. Those smaller systems (like GJ 710) brush against larger (like us) with the outermost former planets being less-bound. But.

I mentioned that our system has a Neptune. Such giants are sometimes visible for us in younger systems, still emitting infrared maybe even still red. High-mass systems are all younger. Up to now I could imagine little reason, oh, a Neptune-mass at a Saturn-like decades-long orbit cannot exist around a midage K. We're simply unlikely to find them soon (for GJ 710 I suppose we'll find out). So we could well be missing available data for Gs and Ks.

Danielski predicts that sliding some older K systems now Pout ~0.5 over to Pout ~5 won't budge their models: selection effects acted as the tip of the iceberg, revealing the existence of much deeper structural diversities between these systems. To that, I see one smaller star with a Jovianlike Pout - ~8 years - and its NAMD is high. One suspects it already did get tugged at by a flyby but retained that planet in a wonky orbit. So I may need to recalibrate my imagination.

Polychroni pipes in for the higher-masses: The greater abundance of material from which planets form around their host stars causes them to be born too large, preventing the system from remaining stable.

For skiffy worldbuilders, this suggests constraints on K "goldilocks" stars' systems. Where they have an ice giant or a super earth outside the HZ, it either formed wonky or else got wonked by "now" (4.5 Gy after first carbon 'stroids). Such has already scattered viable mass in the HZ into uninhabitability. I get the impression this happens a lot. So your constructed K system shouldn't have long-period superearths-on-up.