You've wrapped the classic dangers of time-travel wherein someone from one reality alters the other, wrapped in velvet but its there. Grin!

Maybe throw a good twist in where both realities cross-fertilise (for a change) but hell does not break loose after all simply because timelines are linear even if there are more than one running in parallel.

I've always hated the nonsensical (to me) time-travel hack of someone going back in time, killing Hitler as a baby or leaving a screwdriver in a chariot or some such nonsense and history changes for the worse so the person who did it somehow knows and goes back to prune that branch. It's that concept that bugs me.

Time actually is why we cannot handle the concept of infinity, death being going to sleep and never waking up scares us to our souls, the universe being infinite with distances being measured in light-years, time itself being infinite; even if there were no sentient beings like humans to mark time (we arrogantly like to say our perception of time is what makes us unique amongst the animals) would it cease to exist?

What's so bloody hard about time being linear and multiple timelines being either non-intersectional or, more sensibly, complete bollocks and there is but one amongst associative sentient beings, the very ones for whom time is real.

BTW, the concept of the linear progression of events I believe are perfectly real to creatures other than ourselves; how arrogant we are only because we quantify time in some sort of regular system while then, now, and the repetition of events is good enough for the 17 year cicada and for Hobbes the Ginger Tom to parade the pride at my bedroom door at 0500 every day without failure. It matters not that its the dark of winter or dawn is breaking in summer, its 0500 plus or minus 15 minutes which is a perfectly fine resolution for their purposes.

I digress, of course. A truly dark dystopian tale could be woven around the human achievement of time-travel where the politically correct of the era gain control of the methodology with the expressed purpose of going back and fixing all of what they judge as humanity's wrongs; slavery, the Crusades, the European conquest of the Americas, all theorising any changes to the present would be transparent simply because no-one would know. There would be no awareness of some previous reality, of loved ones never born, the new timeline would be the timeline. So the socially "woke", armed with the technology to go back and right all these wrongs, against all scientific advice. The result would be...?

Can one say that will never happen simply because we are still here with all our past events being grist for our current guilt-mill? Then time-travel is bollocks after all? Then time is linear after all?