Improve structured logging

[matrixbot]

This issue has been migrated from #8683.

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Building on #8588 there's a desire to improve the output of Synapse structured logging.

Currently a "standard" log line would be turned into JSON (this was a curl to /_matrix/client/r0/login to get the login flows, but other logs look similar):

2020-10-29 07:36:00,762 - synapse.access.http.8080 - 315 - INFO - GET-0 - - - 8080 - {None} Processed request: 0.000sec/-0.000sec (0.000sec, 0.000sec) (0.000sec/0.000sec/0) 285B 200 "GET /_matrix/client/r0/login HTTP/1.1" "curl/7.64.1" [0 dbevts]

This would transform to (note that whitespace was added for visibility, normally this would be a single line with no whitespaec between JSON separators):

{
    "log": "- - 8080 - {None} Processed request: 0.000sec/-0.000sec (0.000sec, 0.000sec) (0.000sec/0.000sec/0) 285B 200 \"GET /_matrix/client/r0/login HTTP/1.1\" \"curl/7.64.1\" [0 dbevts]",
    "namespace": "synapse.access.http.8080",
    "level": "INFO",
    "time": 1603971360.76,
    "request": "GET-0",
    "scope": null,
    "server_name": "localhost:8480"
}

A few improvements we'll want to make:

• The log line includes a formatted message, which makes it difficult to search in a structured way.
• Currently logging a message with additional fields requires including the fields twice (using the standard logging flow and the extra keyword to the logger).