Really depends on how often you need to touch your data. Tape has high upfront cost (4-5k $ for a LTO-9 tape drive + ~3,5 $/TB in tapes) but you don't have to worry about archive space anymore. Otherwise, NAS space (if you selfhost) is ~15 $/TB + a server which would also be slightly above 5k right now to store your 300 TB.

You can import Youtube playlists into Jdownloader and download for example your "Liked Videos". You can also use "Google Takeout" to export all you files, playlists and history to CSV.

I use Unraid because everything I want is built in. I also save a lot of power and hard drive wear. Due to the array architecture, all of the HDDs are spun down most of the time. Out of the box Wireguard and automatic remote flash backup are a blessing. Had a major headache from all the NAS OS I've tested over the years and have never regretted purchasing a license. Besides minor problems with macvlan I had zero issues with Unraid within 3 years of usage.

Your HDD will be fine for Unraid just keep in mind that your biggest disk should also be your parrity drive. I also started with an 256GB NVME cache and it helps a lot since no HDD must be running during idle. My Jdownloader download cache, Docker images and appdate remain permanently on the cache drive and I have a plugin to back up its content to the array.

Okay lets say you go the prosumer approach:

1x QNAP QuTS hero TS-h973AX-32G ~ 1300€ each

2x Samsung OEM Datacenter SSD PM9A3 15.36TB, U.2 ~ 1400€ each

3x Toshiba Cloud-Scale Capacity MG10ACA 20TB, SATA 6Gb/s ~ 300€ each

Right at 5k and you get 15TB NVME RAID1 (mirror) and 40TB HDD RAID5 (parity). Without mirror/parity it is 30TB NVME and 60TB HDD raw space.