dual boot – rEFInd broke macOS after removing the partition

I have a problem, help if you can …

I wanted to install Linux, what I did is, I installed rEFInd then I installed Linux on a separate partition of 21 GB. Now I wanted to delete it, so I deleted the Linux partition in Disk Utility. After a reboot, the message "error: no such partition" was received. I have followed several tutorials to find out how to restore it like this one.

However, that did not change anything. After pressing alt on startup, I do not have a boot drive to select, neither Linux nor MacOS.

Then I came across forums suggesting to do fdisk -u /dev/disk0 in the recovery mode terminal. I tried it and I had the following error:

fdisk could not open mbr file /usr/standalone/i386/boot0 no such file or directory

It seems that my partitioning table is messed up. I have also found this. While I was able to run fdisk -e /dev/disk0, I could not find the Partition Inspector because I can not boot to MacOS or Linux.

I should also mention that I use MacOS Catalina (official version), which could have caused problems.

If someone has a clue, that would be really useful …