Really heckling for details, eh?
Of course the canon's pretty loose and open for interpretation, but the general gist I was going for is this:
Anyone who passes through the Void takes on their "true form", which for you (the player) means you can't take a transformation from one world to another, but in a more elaborate sense is the form that reflects the way the person
thinks of themselves.
As people travel between worlds and return to earlier times, they become more aware that their actions don't have meaning or permanence. This causes them to grow more and more detached from their humanity or social responsibility (like Flowey or Rick). Eventually they stop thinking of themselves as human so the "true form" they take when passing through the Void reflects what they now think of themselves. Not all become monsters; the details depend on the individual.
Part of the implication is that holding on to keepsakes can protect one from detachment and transformation, since it gives world-travelers something to attach to outside of themselves.
Why bats or spiders? Well, spiders are solitary, venomous creatures that crawl on "webs", which is a good symbolic representation of someone who travels from world to world alone and hates company...and maybe is aware that the "web" is made by people? Bats are social cave-dwellers and can represent those who formed a "community" among other transformed people but are still detached from their humanity. And both are creatures people are known to be afraid of and reflect the way
they think of "evil".
(Actually, the truth is they just happen to be two kinds of monsters people expect to see in a game and I haven't gotten around to making more. It's not that important. I guess there needs to be a more basic, generic enemy type too.)
Some can become friendly later because they have character development that make them become aware that even if their actions don't have "real" consequence, sometimes it's important to be good to others because it's good for
your well-being (which will be a major theme of my stories at least; I enjoy "counter-nihilistic" philosophies). But they've been transformed for so long that they still think of themselves as giant spiders.
Or maybe some weren't human to begin with... monsters can have children, so what are
they?
It's all pretty loose canon, feel free to play with it, add to it, or contradict it as you like.
I guess I will make better ways of locating a world you have been to before. Using items as transporters could work, though the details need to be worked out.