(It's a great post in general. N.B. that it's also quite old and export templates have been removed from the standard for quite some time after compiler writers refused to implement them.)
TL;DR: Declare your templates in a header, implement them in a source file, and explicitly instantiate them inside that same source file for every type that you want to be able to use them with. You lose expressiveness but gain compilation speed because the template is guaranteed to be compiled exactly once for each instantiation.
Which is to say, "extern template" is a thing that exists, that works, and can be used to do what you want to do in many cases.
The "export template" feature was removed from the language because only one implementer (EDG) managed to implement them, and in the process discovered that a) this one feature was responsible for all of their schedule misses, b) the feature was far too annoying to actually implement, and c) when actually implemented, it didn't actually solve any of the problems. In short, when they were asked for advice on implementing export, all the engineers unanimously replied: "don't". (See https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n14... for more details).
1. You gain the ability to use the compilation unit's anonymous namespace instead of a detail namespace, so there is better encapsulation of implementation details. The post author stresses this as the actual benefit of export templates, rather than compile times.
2. You lose the ability to instantiate the template for arbitrary types, so this is probably a no-go for libraries.
3. Your template is guaranteed to be compiled exactly once for each explicit instantiation. (Which was never actually guaranteed for real export templates).
(It's a great post in general. N.B. that it's also quite old and export templates have been removed from the standard for quite some time after compiler writers refused to implement them.)
TL;DR: Declare your templates in a header, implement them in a source file, and explicitly instantiate them inside that same source file for every type that you want to be able to use them with. You lose expressiveness but gain compilation speed because the template is guaranteed to be compiled exactly once for each instantiation.