I think the only way a creature like bigfoot could stand even the smallest chance of staying hidden for this long in the areas it's sighted in is if it was close to human, for one simple reason; they would have to have human range intelligence. This part really is non-negotiable to me. The intelligence of a gorilla, chimp or orangutan simply wouldn't cut it. They were all discovered by science before the 20th century in areas that are/were more remote than even the most remote areas that bigfoot allegedly inhabits today.
But how close to human intelligence would they have to be? Halfway between apes and humans? 75% as intelligent? 90%? exactly equal? My opinion is that this might not actually be the most useful metric for comparing mental capabilities between different human species. There would probably be many mental tasks that a sasquatch would perform far more poorly than us. But the opposite could simultaneously be true. They could, at the exact same time, also have many mental abilities that are superior to our species. In fact, if anything, they require certain mental abilities that would be superior to ours to have stayed undetected by science this long.
This has been touched a little bit in this thread, but I see Sasquatch's potential evolutionary history as defined by finding a completely different ecological niche to use their high intelligence in than the niche we've been using ours to occupy. What really defines everything our branch of the human tree of life does with our large brains is manipulating the environment to fit our needs. We make tools, clothing, art, and complex settlements out of natural materials that become barely recognizable once the end product is finished. We alter landscapes to fit our needs. We process our food with many steps. We exterminate certain animals that are mortal threats to us. Everything we do that makes us successful involves us carving out our own personalized world from the natural environment. And we are the species that have completely and utterly doubled down on this principle on a scale unlike any other species of humans before us.
A survival strategy like this requires certain mental skills. It requires us to be adaptable. To have the ability to learn any skill that you could conceive of, with enough training i.e a jack of all trades. It requires language on a level that is sophisticated enough to communicate highly abstract ideas. It requires an active imagination. But most importantly, it requires the ability to socially network, to keep track of dozens upon dozens of complex relationships, so that innovation can spread.
Sasquatch, on the other hand, would appear to occupy an ecological niche that isn't based in any way whatsoever on manipulating their environment. Tool use is extremely minimal. What we're only capable of doing so long as we have tools, they can accomplish through brute strength alone. They don't need clothing when they have fur. They don't carve out their environment to suite their needs. They carve themselves to fit their environment like a lock in a key. This appears to be a strange way for a creature with near human intelligence to make use of it. After all, manipulating your surroundings is the most straightforward way of utilizing such a unique trait among the animal kingdom. But if they tried to use their intelligence the same way we use ours, they'd be competing evolutionarily directly against us, and we would beat them at it every time. In the same way that we beat homo erectus, and the neanderthals, and the denisovans, heidelbergensis and florensiensis and any other human that tried competing with us on our playing field. It's only when that niche has been already filled that you should expect the evolution of intelligence to go in a different direction.
So where would that intelligence that a Bigfoot has go into if it's not going into manipulating the environment? It goes into blending into the environment. It goes into stealth, it goes into highly expansive visual-spatial awareness and memory so that they can memorize every single inch of their habitat. It goes into Pattern recognition. It goes to superior motor control and coordination. It goes toward superior perceptual awareness. They have would have a type of intelligence that is highly specialized for their environment. Take them out of that environment and homo sapiens may out-perform them on any metric you can think of with our highly generalized form of intelligence and our ability to learn any skill that we put our minds to. But no matter how hard we train, no person will ever be able to move around the wilderness with the pinpoint efficiency and expert evasiveness that they can, because that is where they spent their evolution tokens on.
As for what their actual lineage is. There are so many things we don't understand about our evolutionary history, and each new find only seems to bring up more questions than answers. The hominin family branch may not so much be a tree as it is a web. With different lineages splitting off from each other and recombining at different times. Sasquatch seems to have traits from all over the spectrum, from australopithecines to homo sapiens itself. If I was forced to speculate, I might say they have their origins in extremely early species of homo, like homo habilis, that travelled to Asia and got multiple injections of new genetic material from later arrivals like homo erectus, heidelbergensis, neanderthals/densiovans while simultaneously splitting off to follow the different evolutionary roads that I've been going on about. Eventually doing some interbreeding with our own species. I have to stop myself here before I speculate too much. But all I'm saying is.....there's still more than enough vacant room on the human family tree to leave some leaves to a species like the Sasquatch, the yeti, yowie, yeren, or alma.