You talk about professional things. How does the Youtuber do it now? The quality of there videos are good.
Again there are many ways to do things. What you asked for (broadcast quality 4K, low compression, many hours of recording...) WILL require multi-thousand $ professional gear. As surprising as it may sound many youtubers do have access to that kind of equipment to work with.
You could also take 2 smartphones, one recording 4K to a 250GB SD card and the other filming the same thing but only doing the streaming and have something to work on, maybe not that long a recording... but meh.
A decent semi-pro solution would be to take a good camera like a Sony A7S + lens and power supply (maybe ~$2.5k total), and record ProRes externally to an Atomos Ninja Flame with a 2TB SSD and power supply (~$2.3k total). Then connect a Teradek VidiU web streaming encoder to the Ninja's loopback output ($700).
That will give you the high dynamic range 4K camera with the best cost/quality ratio, ability to record many hours of high quality log footage for best possible post-production capability, as well as stream a color-corrected version of the footage for pretty cheap in the field.
The equipment can obviously be rented, you don't need to buy 6k of equipment (+another 10k of you want 2 more cam/recording sets in addition to the main cam/recording/streaming set) to do a 2-day project. Most video productions use rented gear, they won't buy something for just one project.
Any less than that and you're quite unlikely to have someone accept your project. They want to be confident about the quality and reliability of what they will do/get, and it's not with a DIY solution with a hacked up RPi that you'll get that when there's perfectly good gear out there to do it. Pro jobs want trusted Pro gear.