"Does potassium really raise cortisol? Are there any published research articles confirming this?"
My google search "effects of potassium intake on cortisol" brought up:
Dreier et al., Effect of Increased Potassium Intake on Adrenal Cortical and Cardiovascular Responses to Angiotensin II: A Randomized Crossover Study, J Am Heart Assoc. 2021:
"... Increased potassium intake lowers blood pressure in patients with hypertension, but increased potassium intake also elevates plasma concentrations of the blood pressure-raising hormone aldosterone.
This argues for aldosterone, not cortisol, being the hormone that does react to potassium intake. That should be accepted knowledge.
My search found only one other study:
Li/Lin, Interacting influence of potassium and polychlorinated biphenyl on cortisol and aldosterone biosynthesis, Toxicology and Applied Pharmacology
Volume 220, Issue 3, 1 May 2007, Pages 252-261:
"Giving human adrenocortical H295R cells 14 mM KCl for 24 h significantly induced not only aldosterone biosynthesis but also cortisol biosynthesis. Pre-treating the cells with polychlorinated biphenyl 126 (PCB126) further increased potassium-induced aldosterone and cortisol productions in a dose-dependent manner, ..."
From both quotes you might infer that as a principle it is acknowledged that high potassium intake is able to increase aldosterone, and that it comes to a surprise to find out the same for cortisol.
Interestingly, both hormones seem to be relevant with Addison's disease (which is primarily known for not enough cortisol only), whereas with Cushing's disease (i.e. too much cortisol) it's only the cortisol. Cp. Wikipedia on Addison's disease: "... endocrine disorder characterized by inadequate production of the steroid hormones cortisol and aldosterone...", and on Cushing's: Aldosterone/potassium not mentioned. However, there seem to be cases to be classified as Cushing's that involve both hormones, see Ren et al., Hypercortisolism and primary aldosteronism caused by ... adenomas ..., 2019,"...Herein, we report a patient with co-existing cortisol-producing and aldosterone-producing adrenocortical adenomas, one in each adrenal gland. ...". On the other hand, Conn's syndrome is defined by too much aldosterone, and cortisol not involved.
Here's my personal hint to it: All this might mnemonically be reconciled by tentatively hypothesizing for the sake of learning that, as cortisol is the first and only hormone to regulate blood pressure after waking up (levels are high in the morning) to raise blood pressure, thus indirectly raising renal filtration and at the same time renal reabsorption. There seems no more than only basic accepted knowledge about the issue of potassium excretion and reabsorption: potassium is freely filtrated, and it is reabsorbed via cells by so called Na+/K+-ATPase (proximal tubuli; to distinguish from the aldosterone exchange of potassium excreted against sodium). Try some search on "cortisol potassium renal reabsorption": the role of cortisol mediated blood pressure on reabsorption of potassium (and sodium) is rather unclear, and it seems no more than a theoretical possibility that cortisol has some direct effect on Na+/K+-ATPase. If yes, that should argue in favour of my own personal approach to Li/Lins's paper: Could surprisingly found increase of cortisol be caused by increase of aldosterone and excessive excretion of potassium (coupled with excessive reabsorption of sodium)? Reabsorption of NaCl, known to be used for plasma expansion, might lead to a rise of cortisol and cortisol induced filtration. Conn's disease (too much aldosterone, no cortisol involved, i.e. contrary to the above no rise in cortisol from reabsorption of potassium) can be differentiated against the findings of the cited study: With Conn's there is no elevated potassium intake (wording of your question). Mnemonically, one might even look upon polychlorinated biphenyl as a functional equivalent of NaCl in that sense (blood volume and pressure).
The above thus tries to reconcile the findings of that single study with traditional knowledge that "elevated potassium" (your question) does not "lead to elevated cortisol" (according to the above: potassium does not raise blood pressure).
The source your question refers to ("Selfhacked") might have - erroneously maybe - not only have exchanged cause and effect but also high and low (to make it right...) as (something Wikipedia on Cushing's does not mention) low potassium levels are known effects of high cortisol levels.
See some bing search about this (not some standard knowledge, I guess)
Cortisol seems to be cause not effect in respect of the regulation of blood pressure and blood sugar, both of which might relate to potassium level (effect not cause):
About the issue of potassium and blood sugar see, e.g., this video on Insuline and potassium relationship. Again, potassium level is considered not cause but effect.
About cause and effect in the context not of blood sugar but blood pressure see, e.g., How does cortisol regulate blood pressure?
"...The exact way in which cortisol regulates blood pressure in humans is unclear. However, elevated levels of cortisol can cause high blood pressure, and lower-than-normal levels of cortisol can cause low blood pressure."
Maybe the statement you quote is based on the known fact that high potassium levels (potassium consumption) are consistent with low blood pressure, implicitely hypothesizing that low blood pressure then leads to cortisol secretion. Conversely, for blood sugar quoted video's issue shows that raised potassium in blood is consistent with high levels of blood sugar which apparently do not call for a raise in cortisol.