Cloning Macintosh HD to a bootable external drive

Hi,

I have to clone my internal drive to an external so that I can update the OSx on my mbp because it is giving me a real hard time with many things. The point is I have software that won't run with Monterrey os and I need that software to work, and someone suggested to do the cloning. So far I have successfully installed OSx on this external ssd and it runs ok, but I cannot update that os and I have looked for a method to clone my drive onto the external drive but so far I have hit the wall over and over. My mbp is a mid 2015 model, with 16gb of ram and 512 on the drive, so in theory it should be able to support Monterey. Also I would very much like to start the internal drive from scratch and every file, photos and so on that I have accumulated thru the years leave it on the external bootable drive, is that something that you would recommend?