The talks were by Jason Turner, who has an ARM emulator implemented entirely as constexprs and a test suite that runs at compile time (so if it compiled, the tests passed). Obviously for actually interacting with it, its not running at compile time, but the logic has the ability to run at compile time, which is pretty cool.
"Old school" is asically the programming languages that originated in the 70s-80-90s. An incorrect but an illustrative way to describe error messages for them is "The programmer needs to suffer". They are any combination of cryptic, terse, complex, exposing internal machinery of the compilers and linkers etc. There are many reasons for this: computers were not powerful enough to afford better code analysis, parsing, backtracking etc; the users of the tools also knew the tools and could tinker with them etc.
"New school" is from late 2000s on. I usually say it started with Elm. Clear messages pinpointing the exact problem, solutions to problems inside error messages, error clarity as one of the priorities in language/compiler/tool design.
Category grammars were much better but more resource demanding, just like proper ASTs instead compiling as one goes.
Ironically there were already some attempts to Smalltalk like tooling for C++ back then, but again as you mention too much resource constraints.