Humphrey Bogart had a stable of great ones, who were sometimes stars but more often supportive - Claude Rains, Sidney Greenstreets, Peter Lorre…
Character actors are a little different from other kinds of Supporting actors. A character actor was type cast into a certain role; police officers, reporters, “mothers of the star”, or something. Character actors flourished during the Depression, when a steady paycheck from a studio was crucial. They were not trying too hard to be major stars. They could be counted on to not steal a scene. You could put Thelma Ritter in a movie, and right away the audience knows a lot about her character - trustworthy, source of good advice, often a rock of stability, steady background against whom the starlet could be contrasted as she goes through changes. The audience had seen Thelma in dozens of similar stories so her “backstory” is established without taking time from the plot.
A “Supportive” Actor might be someone on the rise, or it might be some actor who is past their prime but still marketable, like Edward G. Robinson. Unlike character actors, who accepted or even sought out typecasting, supportive actors complain about it and turn down certain roles too much like their last one.
I suspect character actors disappeared mostly after the 1960s. It’s frustrating that I can picture this or that character actor from countless movies, but when they are on screen I can’t usually remember their names. Nowadays I rely on Wikipedia or IMDB. This is what I do instead of needed work around the house, spiritual and corporal works of mercy, etc.