"The question is the following: what is the nexus (if there is one) between the oort cloud and the comets?"
This report and 22 page arXiv paper is the most detailed I have read on the Oort cloud and comets in our solar system. 'Astronomers calculate genesis of Oort cloud in chronological order', https://phys.org/news/2021-06-astronomers-genesis-oort-cloud-chronological.html
My observation. Simulations require assumptions about initial conditions or starting conditions to calculate. This statement is a good example of assumption in the model. "The Oort cloud, the Leiden simulations confirm, is a remnant of the protoplenatary disk of gas and debris from which the Solar system emerged some 4.6 billion years ago. The comet-like objects in the Oort cloud come from roughly two places in the Universe. The first part of the objects comes from close by, from the Solar system. These debris and asteroids have been thrown out by the giant planets. However, some of the debris did not succeed in doing so and is still in the asteroid belt between Mars and Jupiter. A second population of objects, the Leiden astronomers conluded, comes from other stars. When the Sun was just born, there were about a thousand other stars in the vicinity. The Oort cloud may have captured comets that originally belonged to those other stars." If this assumption is not correct for the origin of the Sun, the simulation is not valid or may have other issues.
Reference, “Oort cloud Ecology II: The chronology of the formation of the Oort cloud, https://arxiv.org/abs/2105.12816
, 26-May-2021. "We present a chronology on the formation and early evolution of the Oort cloud and test the sequence of events of its formation by simulating the formation process in subsequent amalgamated steps."
On page 3 of the report the Oort cloud mass estimates are provided. “The mass of the Oort cloud is estimated to range from 1.9Mearth (Weissman 1996) to 38Mearth (Weissman 1983). These estimates seem somewhat on the high side when compared to those based on numerical simulations, which arrive at 0.75 +/-0.25Mearth (Brasser 2008) to 1.0 +/- 0.4Mearth (Fernández & Brunini 2000). With a typical comet-mass of a few times 10^12 to 10^14 kg (Rickman et al. 1987; Sosa & Fernández 2009, 2011) the Oort cloud contains 10^12 comet-sized objects. Interestingly, this estimate is comparable to Oort’s original estimate of ~ 10^11 objects (Oort 1950), and to the density of interstellar asteroids (Engelhardt et al. 2017; Portegies Zwart et al. 2018; ’Oumuamua ISSI Team et al. 2019; Pfalzner et al. 2020).”
My observation. Without the Oort cloud, short period and long period comets including comets that make only one perihelion pass by the Sun today, do not fit the 4.6 billion years old solar system model based upon meteorite radiometric dating methods. Comets in the solar system today suggest a much more recent origin and much younger age in the solar system if there is no migration from the Oort cloud for many comets observed today. Direct observations of the Oort cloud remain elusive unlike direct observations of stellar parallax for stars or observations and measurements for asteroids in the solar system today like 4 Vesta or the Galilean moons at Jupiter.