Windows 11 downloaded and almost finished installing, but then restarted and went back to downloading again

When a computer is upgraded and fails it typically records an error code and message in the log files.
These can be checked if needed.

1) Run setupdiag: https://learn.microsoft.com/en-us/windows/deployment/upgrade/setupdiag
Post a share link into this thread using one drive, drop box, or google drive

2) List any of these non-Microsoft software:
a) antivirus
b) firewall
c) drive encryption

3) Run the Windows 11 compatibility tool or PC Health Check Application:
https://www.microsoft.com/en-us/windows/windows-11
https://aka.ms/GetPCHealthCheckApp
Post images or share links into this thread

4) Run the V2 log collector and post a share link into this thread using one drive, drop box, or google drive:
https://www.windowsq.com/t/bsod-posting-instructions.17/
https://www.windowsq.com/resources/v2-log-collector.8/
https://www.tenforums.com/bsod-crashes-debugging/2198-bsod-posting-instructions.html

5) Open administrative command prompt and type or copy and paste:
sfc /scannow
dism /online /cleanup-image /restorehealth
chkdsk /scan

Post images or share links of the commands with results into this thread.

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Please remember to vote and to mark the replies as answers if they help.

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I recommend you to try manual upgrade and see if it helps:

https://answers.microsoft.com/en-us/windows/forum/all/upgrade-from-windows-10-to-windows-11-using-iso/cc730f52-cd85-45d6-8b52-c10d3ff2d67e

There can be many issues during the download of Windows 11 installation files, for example ISP , or Disk space issue or your Antivirus may block some files during download etc.

I will suggest you to Install Windows 11 using .iso file as per below Microsoft article.
https://www.microsoft.com/software-download/windows11

--If the reply is helpful, please Upvote and Accept as answer--