Spinning hard drive? or SSD?
Either one is "missing", so you will need to replace the drive.
I think you have a spinning hard drive, that worked "good enough" to get to the Windows system boot blocks, but no further. A failed SSD would probably not get that close to working.
Yes, you can run with an external drive. You may want to remove the internal drive, just in case it begins to interfere with anything else that boots your system. In other words, I wouldn't trust a "dead" drive that might suddenly start working just enough to give you problems.