Earlier quoted context omitted.
Do we? In Germany, Linke (Left), is by far strongest in the former DDR, and it came out of PDS, which again was the successor to SED - the ruling party of DDR. It has merged with some other groups, and appears fairly thoroughly "reformed" to the extent that they're too centrist for many socialists, but the imbalance between its support in the East and West remains. It varies a lot by country, seemingly both coming do…
Linke, or DDR, is now fabian (democratic) socialism.
And, by the way, Fabianism is virtually unknown outside the UK today other than in small pockets in the English-speaking world, though it had such unfortunate effects as inspiring the creation of the Ba'athist movement (Saddam Hussein and the Assads were/are Ba'athists), and also inspired quite a few other leaders of former British colonies, many of whom thankfully made better leaders.
Most places outside the UK, when talking about democratic socialism you can be talking about anything from libertarian communism to social democracy - the term generally only exclude Stalinist/Maoist parties. Many communist parties have explicitly used the term in order to signal lack of support for Stalinism. But most "democratic socialist" parties are to the left of the social-democratic parties though the latter also use the term with some regularity.
Though you're right that they are increasingly gradualist like the Fabians.
Most social democrats outside the UK see Eduard Bernstein as one of their main sources for their gradualism, not the Fabians, in part because largely unlike Labour in the UK most of the European social democratic left as well as many other places started as communist parties and split and/or reformed (most of them in the period between the October Revolution and Stalins decree that Comintern member parties were to be obligated to accept orders from the Soviet Union), and Bernstein as a friend and associate of Marx and Engels who continued to support many of their views and goals even as he rejected the need for revolutions was able to gain far more support than the Fabians that had pretty much no presence other than in the British Empire.