Is the 5D Mark III a good DSLR for both photography and videography in 2020? Does it support features such as tracking or continuous AF in video mode? I did some research but I didn't find a clear answer. Last question, how is the noise level at high ISO? I had a 5D M3 in my hand for 5 minutes today and I did some test and I scrolled in the menus but I'm not sure if I will buy this one or the t7i.
The 5DIII is great for photography. The improvements in the 5D generations for photography are mostly in high iso, homogeneity in noise and definition. It has 3 AF in video: quick (through optical viewfinder and classical AF), AF (you put the zone and ask for focus), and AF with face tracking. It's OK but far from the dual pixel AF you get in 5DIV, Canon R series, and Canon cine cameras (C200, C500II, etc), which is a big game changer in speed and accuracy: try it. High iso noise is between the 5DII and 5DIV. It's not noticeable up to 6500 and barely starts to be visible at 12000 ISO.
If you're into high quality photography and video and light hardware, you might want to look at Canon R, esp. the R5, which is about to appear and sounds very promising. Without the optical view finder and mirror, and with telecentric optics, you get something very interesting in terms of weight and image quality. Unless the optical viewfinder and AF speed are important.