We do this to prevent foot guns. The default config uses a MemoryFilter,
but users are free to change to logging to files directly. If they do
then they have to ensure to set the `filters: [context]` on the right
handler, otherwise records get written with the wrong context.

Instead we move the logic to happen when we generate a record, which is
when we *log* rather than *handle*.

(It's possible to add filters to loggers in the config, however they
don't apply to descendant loggers and so they have to be manually set on
*every* logger used in the code base)