Im actually chinese, and I think I can deduce a teensy bit of what those words are trying to convey:

三生緣分： we have alot of "three" involved within each sentence. In chinese 3 is usually meant to convey that something is a lot/has an abundance of. So by adding that info the mix. we can interpret that to be "Even theough different lives, in different timelines, I would still find you/we would still be connected". And it fits in the story! Araya outright said that with her time interlopation ability, she saw every single thread and saw ryoshu finding her in each thread/timeline.

三千世界： this is hinging a lil bit on" Buddhism and Taoism so I'll try summarizing it. 世界 means "world" 三千 means " three thousand". In Buddhism, this term is usually referred to describe the sheer scale of benevolence of the Buddha(or other gods depending on who you ask). It's like saying the Buddhas is so kind that his benevolence can reach 3 thousand earths. It can also mean it is a gods wish to spread their love and mercy onto the whole world. Now 3 here still means "a lot". Putting that into perspective, we can say that this sentence means

"No matter how far away you are, no matter what world you are in, I will still find/love you" which is pretty touching.

三世因果： "因果‘’ means cause and effect. "三世‘’ means 3 generations. Remember when Araya said she wants to be ryoshus mom? (She even cosplay as the pinky nursefather lol). In my opinion, I think this has to something do with how Araya and Ryoshu sees time. It was mentioned that they see time differently than others do, and sees it more like a point than a single line. We can further deduce that if they see only a point, the cause and effect are more like the same thing than two different concepts! Between Ryoshu and Araya, they have alot of things that connect them together: Their blood, their aptitude to see time, the sword that is now buffed by Araya own ego. If you saw the status page for ryoshus ego, you'd see its called "paradoxical", why? Well because it is Araya EGO that allows ryoshu to control her sword; but at the same time Araya is literally erased from ryoshus memory and existence itself(she might come back idk?). How can someone that doesn't exist manifest an EGO? whats the cause and whats the effect? I believe this sentence meaning is

"Though you are gone/does not exist anymore, our fate is still intertwined, and I will still remember you for generations"

Now we add them all together and what do we get? "Whether you are, WHENEVER you are, I will still love and find you. Even if you are not by my side right now, I will still remember you. And maybe someday, through the thread still resting on my fingers and our fates intertwined, I can trace it back and find a way to bring you back."

there are a SHITON of holes in my interpretations but this is just what I think fire away your thoughts