The pace of change is fast, but only because we are still dealing with the consequences of the scientific and industrial revolutions. I now think of all technologies past ~1800 as "modern". Basically you should learn all of it to some degree.
19th century machinist skills? Still useful and valid. The basic design of a lathe has not changed since the late 1700s.
COBOL from the 1970s? Nobody is going to throw away so much working code. The first generation of programmers is dying off only now, trust me this stuff is going to be around for a long time. Same deal with C / C++.
Oil burner heating from the 1940s? It's a convenient upgrade from the prior coal technology (much easier to pour oil than bunker coal). Most of the systems installed are still there and running. Diesel fuel / jet fuel / heating oil is still probably the most convenient to use energy source.
A slight change to how web technologies work? Really not a big deal..
AWS? Their servers are still basically IBM PCs.