"Invalid partition table!" error after attempting to upgrade to Ubuntu 21.04 alongside Windows 8.1

Question

On my Dell Inspiron 5558 I used to have the double booting of Windows 8.1 alongside with Ubuntu 18.04.5 LTS. Now I decided to upgrade the Ubuntu 18.04 to Ubuntu 21.04. However, I met some technical problems and I can not run my Windows 8.1 anymore, just live Ubuntu 21.04. And one of the problems is this error

Invalid partition table!

My question how can I repair now everything? Though I can again possess double booting of my old Windows 8.1 together with the new Ubuntu 21.04. Or now I have to start from scratch with a new Windows and a new Ubuntu (I hope not...).

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Here are the steps that I executed and brought me to a failure:

1. Creating with Rufus a bootable USB drive of the ubuntu-21.04-desktop-amd64.iso

2. Running this USB in BIOS as UEFI Boot (Boot mode: UEFI, Secure boot: Off) and following further the steps on the Ubuntu 21.04 installation

3. I decided to have the same partition of my SSD as I had before (swap, efi, /, and /home under the hood of /dev/sda4), see image below

4. Unfortunately, almost on the last step I encountered the first error, see image below

Executing 'grub-install/dev/sda' failed.
This is a fatal error.

5. After all I wanted to check my Windows, and this time I could not access my Windows. I got such response, see image below

Invalid partition table!
error: unknown filesystem
Entering rescue mode...
grub rescue >

6. The same thing happened here, after restarting my PC.
   I got the same issue:
   

error: can't find command parttool
error: can't find command drivemap
error: invalid EFI file path.

Press any key to continue...

7. I decided to run the installation process of Ubuntu again with formatting the partitions where was the old Ubuntu. At that time I could see my SSD in the UEFI boot menu, see image below.

   Then via the Ubuntu Live and GParted I checked what is going on with my partitions

   Thereafter I formatted the old partitions, to be able to install the Ubuntu 21.04 again

   But this brought me to the same errors, described in steps 4 and 5.

8. I also tried to make from old Ubuntu partitions a normal NTFS drive and simply running just Windows Nevertheless, after restarting the computer I got an explicitly described error
   

9. I ran also the Dell's Support Assist and ended up with this response

I tried these solutions:

• Invalid EFI file path
• "Unable to install GRUB in /dev/sda" when installing GRUB
• https://www.dell.com/support/kbdoc/en-de/000132051/how-to-fix-an-invalid-partition-table-error-on-a-system-with-a-ssd-solid-state-drive?lwp=rt
• https://www.youtube.com/watch?v=BdLLjohm7_8

Hence I do not have that my experience with Linux and partitions I barely understand what shall I do now...any suggestion are appreciated. and welcomed.

Luckily, I can access my data on the Windows 8.1 through mounting the drives in Ubuntu 21.04 Live.