Poking around, there are a lot of individual studies of varying size and quality suggesting close associations between visceral / perirenal fat and hypertension. What you really want to see are large-scale metastudies and expert reviews seeking to adjust for confounders, biases etc over large datasets & support causality, and on a quick look I still don't find much along those lines.
But this seems like a detailed recent review:
https://academic.oup.com/ckj/article/17/1/sfad282/7419873
In 1988, Gerald Reaven hypothesized that insulin resistance was the key factor in a group of metabolic disorders, later called ‘Syndrome X’, which included impaired glucose tolerance (IGT), hyperinsulinemia, high triglycerides, low high-density lipoprotein cholesterol levels and hypertension [23, 24]. Then Norman Kaplan identified also central obesity as a key driver of CVD and defined the cluster of visceral obesity, IGT/insulin resistance, hypertriglyceridemia and hypertension as the ‘deadly quartet’ [25]. For more than 30 years, insulin resistance and hyperinsulinemia-dependent overstimulation of sympathetic nervous system (SNS) and increased renal sodium reabsorption have been considered as primary mediators of elevated BP in metabolic syndrome and obesity. However, strong experimental and clinical evidence is available to suggest that obese subjects can be normotensive despite severe insulin resistance and hyperinsulinemia [26]. Indeed, increased renal sodium reabsorption and consequent expanded plasma volume sustained by compression of the kidney by perirenal and intrarenal fat and systemic/renal SNS and renin–angiotensin–aldosterone system (RAAS) overactivation have been subsequently identified as major factors mediating the initiation of hypertension in obesity [5, 26]. On the other hand, it is clear that in the long term, insulin resistance and hyperinsulinemia, and consequent hyperglycemia and dyslipidemia, interact synergistically with elevated BP in the induction of renal and vascular injury that in a ‘vicious circle’ contribute to further worsening of hypertension and increased risk of renal and cardiovascular complications.
This suggests that (a) kidney fat can indeed be a main driver for hypertension but also (b) it can happen in the absence of insluin resistance, which suggests that you can get kidney fat without liver fat, at least in the short term.
Anyway, it's all very interesting.