NAS are essentially small computers made for connecting a lot of storage and with a fancy OS that can be configured with a browser.
So the real question between the NAS or a custom build is how much time do you want to spend being a sysadmin. NAS mostly work out of the box, you can configure them to autoupdate and get notification only when something important happens. While with a custom build everything is completely on your own. Are you already familiar with some linux distribution? How much do you want to learn?
Once you answer the previous question, the next is about the power. To store files on the network you don’t need any big CPU, on the contrary, you may want something small that doesn’t cost too much in electricity. But you mentioned you want to stream video. If you need transcoding (because you have a chromcast that wants only video in a specific format for example) you need something more powerful. If you stream only to computer there is no need for transcoding because they can digest any format, so anything will work.
After this you need to decide how much space you need, and what type. NMVE are faster, but spinning HD were still more reliable (and cheaper per TB) last time I checked. Also, do you want some kind of raid? RAID1 is the bare minimum to protect you from a disk failure, but you need twice as much disks to store the same amount of data. RAID5 is more efficient but you need at least 3 disks. Said so, remember that RAID is not backup. You still need a backup for important stuff.
My honest suggestion is to start experimenting with your raspberry and see what you need. Likely it will fit already most of your needs, just attach an external HD and configure samba shares. I don’t do any automated backup, but I know that syncthing and Syncthing-Fork are very widely used tools. On linux you can very easily use rsync in a crontab.
If you want an operating system that offers you an out of the box experience more similar to a commercial NAS you can check FreeNAS. I personally started with a QNAP and have been happy for years, but after starting self hosting some stuff I wanted more flexibility so I decided to change to a TerraMaster where I installed a plain Debian and I’m happy with it, but it definitely requires more knowledge and patience to configure and administrate it.
You can configure caddy to use 80 and be a reverse proxy for both the services, serving one site or the other depending on the name (you will need a second DNS entry pointing to the same IP). about not exposing 443, I really doubt that caddy can automatically retrieve SSL certificates for you if not running on the default port. Check the documentation, if I’m right either you open an empty website on 443 just for the sake of getting SSL certs to run https, and manually configure the other port to do the same, or you get the certificates manually using the DNS verification (check let’s encrypt documentation) and configure caddy to use them.