How to update a MacOS installed in an external SSD beyond Sierra

My 2015 MacBook Pro 13's internal SSD died during an update yesterday. When I try booting it says there are no drives to boot from. I used Internet Recovery and there is no sign of the internal SSD anywhere.

So, I plugged in a brand new 1 TB external SSD, it installed El Capitan and it worked perfectly. I updated it to Sierra without issues but when I try to update it further to High Sierra and beyond I get a message saying the disk doesn't have a firmware partition. I google this issue and it seems that MacOS versions released after Sierra require a working internal storage disk in order to install. Is it possible install the High Sierra in a USB stick and use that to run the installer?

Edit: It was running Mojave when it died, I had noticed that it was running much slower than usual which is why I tried updating it.

I was also wondering if it is possible to install Windows 10 in a different partition of the same external SSD since the stuff I need for work runs on it, however I can't get bootcamp to work without a internal SSD either.

Below are some possible solutions.

Replace the internal drive. This website shows replacement drives and links to installation videos.
Use another Mac with a working internal drive to upgrade the external drive to High Sierra or Mojave. Once completed, you Mac should boot from the upgraded external drive.
Try upgrading directly to Mojave, thus bypassing High Sierra.
Use an virtual machine to update to High Sierra. Here, the virtual machine would have a virtual internal and a physical external drive. Once the upgrade is complete, you should be able to boot from the upgrading external drive using the physical Mac.
Many answers explaining how to install Windows 10 on a external drive have been posted here at Ask Different. You could start with this answer. Since you have El Capitan installed on the external drive, you probably will have to adapt an existing answer.