I own a i7-9700k and an RTX 2080 Founders Edition; not a 2080 Ti, but I think I can help.
First, the 9700k shouldn't bottleneck you at 1440p. I run mine with a H115i AIO and have an all core boost clock of 5.1 Ghz and it works great for me. It might be possible for you to bottleneck at 1080p if you were pushing for really high fps, but I seriously doubt it at 1440p.
Secondly, I would a) recommend the i9-9900k over the 9700k, and b) a tenth-gen processor even more strongly than the 9900k. Why? It doesn't make sense for me to upgrade my motherboard and CPU to the latest and greatest because it is only a generation old and still works very well. However since you are saving up to start fresh and obviously can afford to spend more than most (you're asking about a 9900k and 2080 ti after all), you should future-proof yourself by getting the most current hardware. Apparently the i7-10700k is similar in performance to the i9-9900k while costing 9700k money. That's an appreciable gen on gen improvement. Whether you go 9900k, 10700k or 10900k, having hyperthreading enabled in your CPU is a solid boost and will be valuable down the road as games start to scale more and more over multiple cores and threads.
The 9700k is solid, no doubt about that, but in retrospect I wish I had gone for the 9900k so I just want to save you that same regret.
Also worth thinking about is the impending release of Ampere. Just as 9th vs 10th gen Intel chips have seen a solid gen on gen improvement, we can expect a big jump in performance to the 30XX series of Nvidia chips. I'm going to be the first in line to buy the 3080 Ti or whatever they're going to call it. If you can wait and keep saving up until September/October, I think it'll be worth it.