I am trying to use a chromium extension that requires a .deb (64) file to be installed. I know that it got a different system target, but the developer didn't made a version for ARM based systems. And I wonder if there would be any manner to circumvent the problem, since the extension is vital for the use I have in mind. When I try to install manually, the system asks for lib6. But I already installed all possible lib6 dependencies, and Raspberry OS (32) keeps asking for it.
"Deb64" is not a real thing. I presume you mean amd64, which is the debian tag used for what would more commonly be considered x86-64, the Intel/AMD 64-bit ISA (sometimes shortened to x64). Presuming this extension is closed source, it could be that the developer just refers to the package that way to indicate a linux viable version.
There is also in this context arm64, which is the 64-bit ARM ISA (sometimes referred to as "aarch64"). This is viable on a Pi 3 or 4 running a 64-bit OS. There is a beta 64-bit RpiOS available and it seems to be fine. I have been using it for a while now with no issues, albeit headlessly -- so, I have not tried chromium, but I am sure we would have seen gripes about that here if there were a problem. There are other arm64 distros available for the pi as well.
However, x64 and arm64 are not compatible. You cannot convert binary ISAs, and there is no way to run x64 stuff on any model of Pi, so most likely you are out of luck. If there is an arm64 version you could try that. If the source code is available, it could possibly be compiled to that.