What you have to do as a developer is try to keep up with the hundred new things, possibly dabble in them to see what they are, and decide for yourself how much effort you want to put into that particular "thing". You have to use judgement or you will burn yourself out.
I never bothered with Pascal. I learned enough Java to be dangerous, but it didn't really apply to my problem/solution domain. I did learn C++ and also learned to distinguish between when a solution looked like an object (C++) and when it did not (ANSI C). If anyone tells you to 'always use C++' ignore them.
I learned Perl, because I found it more useful than AWK for large problems, but AWK still reigns supreme for 'one liners'. Then I learned Python, and discovered that the problems then fall into Python or AWK. I rarely use Perl anymore.
I tried my hand at Go. I don't find it very satisfying. I am looking at Rust.
Everything else I have ignored, by virtue of choosing what problem domains I am interested in solving.
So that software engineers are not screwed, not by any margin. Just choose the problem/solution domain that you want to work in, narrow down the tools you want to be competent in, and move forward. Try to avoid the 'Look! A Squirrel!' response mode as much as possible, but do poke your head up to see what the world is doing on occasion. But be aware, a lot of it us useless noise.