What a coincidence! DIY Perks published a video about a similar project on Oct 31, 2020.
DIY Perks: Building an artificial sun that looks unbelievably realistic…
If you prefer something you could put together in 5 minutes, you could get a softbox lighting kit and a 4 pack of YujiLights™ High CRI 95+ LED Corn Bulb E27 36W G02 5600K for Studio Softbox.
https://store.yujiintl.com/products/high-cri-95-led-corn-bulb-e27-36w-g02-3200k-5600k-for-studio-softbox
Lensvid did this and they wrote a blog post about it.
Lensvid: Super High CRI LED Bulb Review (Yugi Lights 36W Bulbs)
If you do this, you could probably tint mix 2x 3200K and 2x 5600K to get 4400K with rosy tint.