Everyone makes incest jokes about Adam and Eve and their children but they never mention that there was another woman named Lilith (Adam's first wife) who would have added variance to the gene pool.
Two things about that (overanalyzing your shower thought):
Geneticists have what they call the "50/500 rule," which basically means that you need at least 50 people to avoid inbreeding, and at least 500 to avoid genetic drift. So while three people are 50% better than two, it's not going to come close to avoiding inbreeding.
If you read up on Lilith, including your Wikipedia link, you'll see her name only comes up once in the Bible, and it's not as Adam's wife. All the stuff about her comes from other things, including Babylonian and Mesopotamian writings, and lots of folklore from the middle ages. And at that, she's sometimes Adam's first wife, with different explanations about what happened to her that really in her not coming back to the garden, or she's a demon. So there's not much likelihood that she's contributing to the gene pool.
The chances are around 260k to 1. Factoring Eve's lack of a second sex chromosome, (unless she has swyer syndrome) the equation would be 1/((22²+1)(23²))≈0.00039%
As you mentioned it depends on chromosomal differences, I just provided the probability of it actually happening.
And, yes. Barring any mutations or trait selectivity, if we all came from the same individual, there would be about 30k identical people of the 8.1b population.
The only counterpoint i can see is that god is (honestly, at best WAS) infallible.
So god made 2 perfect humans who cannot inbreed as there are no defective genes.
At some point down the line, mutations came in and introduced possible genes that could combine/dominate to produce inbreeding.
If we are accepting the premise of 2 original humans, why not 2 perfect original humans.
If God made eve from adams rib, why not have them be genetically perfect.
But Im sure there is some science i am missing where a huge genome analysis has shown that "perfect" genes have never or could not ever exist.
And, tbh, this might as well be all science fiction based on a bunch of made up stories.
It all makes more sense when you consider these stories in their historical social context. They're a compiled bundle of stories from various religious traditions that were kind of grafted together to form one monotheistic state religion to help unify the country. So you find stories from both north and south Judah for example, the two creation myths in Genesis. And you see the monotheistic god referred to by more than one moniker because they were originally different gods.