Draft: Switch to JSON log format as it’s more widely supported out of the box

Log processors often ship with inbuilt JSON parsers, but at least some
of them, notably Azure Log Analytics, don’t come with a built-in logfmt
parser.

Note that we’re not enabling dict_tracebacks, which could provide
structured exception traces, but there doesn’t seem to be sufficiently
mature support for that format at the moment.

Signed-off-by: Andrej Shadura <andrew.shadura@collabora.co.uk>