Digging into some deep speculative fiction here rather than pure fantasy.
An Idea I've always I liked that can be extended to include tectonics is deep speculative biology, creating links between plants and animals with ancient evolutionary connections with distant relatives across former continents, within this world extremely slow evolving or slow living creatures could experience time differently to us, to our eyes they might seem completely static like rocks or trees but to them they are a thriving and active community.
From that you can have civilisations that have existed in some form across hundreds of millions, or even billions of years with notable epochs in their long history being related to points in time where different land masses were connected, causing major societal upheaval and rapid evolutionary shifts, but also access to potential new resources and technology.
You could have one group of people on an isolated plate that over hundreds of millions of years contacted other landmasses and either settled them causing new disparate groups to form, or met with existing other groups and shaped their future by passing on some technology or resource.
Imagine an overwhelmingly large planet with uncrossable oceans, how they're uncrossable could be expanded upon, but imagine that travel across this ocean is completely impossible or impracticable in some way, perhaps flight is also impossible to extreme gravity, high technology may be impossible due to resources. plate collisions are rare due to the immense size of the planet and the small size of the landmasses in comparison so the only way these people have ever come into contact with other civilisations or non native species is through the slow movement of their plates, they have remnants of stories from their deep history, they have long melded into mythology, possibly becoming their creation myths.
So a short prompt for a story or role play of some kind could be:
An outcast scientist has created a piece of equipment to peer into the distance and he sees what appears to be land, it seems to be moving towards them, fast. He tries to tell the ruling priests that a landmass is approaching and will make contact with them within a generation, they scoff as the prophecies say it will be a thousand generations before the next "meeting".
One possible source of inspiration would be the Zanclean flood, where the Mediterranean suddenly got connected to the Atlantic ocean and filled up quickly. Plate tectonics are cool in that way that they happen very slowly but some of their effects are extremely sudden.
xkcd.com/time is an interesting story about this event
I had originally done quite a bit of tinkering with tectonics for my world's map, but found I wasn't getting the results I was looking for/getting frustrated with just how much was involved to feasibly replicate it.
I found my fantasy solution: while the world was still molten hot from its creation, great elder beasts were plopped down on it, and in their ensuing melee, the mountains, hills, oceans, and trenches were formed. Their now dead forms can still be found on the world, many of the largest mountain ranges, island chains, and deep sea trenches found along their breadth.
I didn't really answer your question, but you had me thinking of bashing my head against my keyboard for a couple of weeks some time ago!
I've made many worlds with plate tectonics, it's my favorite method to make maps!
It's outlined very well in this book, my favorite worldbuilding book.
It takes some time, especially your first go at it, but I think it's really fun and adds a lot of realism to the geography.
As someone who isn't as hardcore about realism, my approach is just to use it as a sort of base to figure out where stuff goes (for example, determining where mountain ranges and resources are), but I don't bother adhering too strictly to it and if it comes into conflict with another idea I have I'll usually prioritize whatever that idea is.
For example, I wanted a desert with a mountain range along its eastern and southern sides. So I did it backwards, first drawing the map then figuring out some plausible plates for it and using those to come up with the surrounding areas that I didn't have plans for.
Though actually I'm not sure if realistically my world should even have plate tectonics, since it takes place on a terraformed moon, and AFAIK smaller planets/moons tend to have less active cores. I probably should research that a bit.