I have an Apple TV 4K and a Raspberry Pi 3 B (RPi3) connected to a switch. The switch is connected to my router.
I then have a 1TB Samsung 860 SSD in a USB3 enclosure which is connected directly to one of the USB2 ports on the RPi3.
The SSD has a very low power consumption and the RPi3 is able to power it directly without any problems. This is most likely not going to be the case with the 2 x 2.5" drives (presumably HDDs) you mention. If you are lucky, you might be able to run a single 2.5" HDD off a RPi3 with some tweaks, but you really should use a powered hub or use drives that have their own power supplies.
The limitation is not going to be the USB3 interface on your HDDs but the USB2 one on the RPi. At best, you are going to get 10MBps (< 100Mbps). The Raspberry Pi 3 B+ has a “Gigabit” Ethernet port, but it is actually hanging off the USB2 hub and practical bandwidth is more like 300Mbps. But this has to be shared with USB2 traffic from the HDDs so you can actually find yourself worse off using an RPi3+ instead of an RPi3 or RPi2.
I am running LibreELEC (Kodi) on my RPi3 and I am simply exposing the SMB protocol so I can connect to my SSD from Apple TV 4K.
I do not have a 4K TV or any 4K material so I am only using this setup for 1080p (or less) material, but 1:1 Blu-ray ISO rips work just fine. I should mention that though the transfer speed is fine for streaming, it might not be as fast as a Gigabit connection to a “real” NAS when it comes to initial buffering or skipping.
When I need to reorganize files on my SSD I just unplug it from the RPi3 and plug it into my PC so I can get full SSD/USB3 transfer speeds, i.e. >400MBps. I suggest you do the same. Transferring large files over a 100Mbps network connection is just painfully slow.
I suggest that you do a Google search for “sbc nas” (without the quotes). There are plenty of articles on the subject and options, including Odroid HC1/HC2. You might also want to consider a Zidoo X9S (old model, but cheap) or Zidoo Z9S with both are media players (play BD and DVD ISO rips with full menus) which double as NAS servers with SATA and USB3 connectivity.
If you still wish to use a Raspberry Pi just because you already have it, and you want to use real NAS software rather than just “my” LibreELEC/SMB “solution”, you can install OMV (OpenMediaVault) on it.
You might also consider buying a cheap NAS without disk such as a Synology DiskStation DS119j and move your 10TB HDD from its enclosure (bye bye warranty) to the NAS. That would give you a setup similar to what most everyone else is using at a very low cost.
But again: Using a RPi2/3 as a NAS server for your 10TB HDD (or your 2.5" HDDs using a powered hub) will probably work, but you don’t really want to use such a connection for organizing your files.