Way to inject context using middleware?

I'm registering some middleware for my REST API and I would like to use it to connect to a database and provide the database client to the handlers. However, I can't figure out a way to pass the new object along to the handlers. I assumed it was as simple as calling the `get_response` function with more parameters and defining my handlers to accept additional variables, but now I realize there is more going on before my handlers get called. I then looked into modifying the event dictionary in the Request object as a workaround, but the event is not an exposed property. How can I do this? Other API frameworks that I've worked with allow middleware to modify request objects directly as a way of passing information to the request handlers. I don't see a way to do that here.

To detail what I expected:
```
@app.middleware('http')
def inject_context(event, get_response):
try:
db=boto3.resource("dynamodb", region_name=AWS_REGION).Table(TABLE_NAME)
ctx = { "db": db }
return get_response(event, ctx)
except (ResourceLoadException, ResourceNotExistsError) as err:
{ ... } # LOG AND RETURN 500 RESPONSE

@app.route("/list/things", methods=["GET"], content_types=["application/json"])
def run_get_account(event, ctx):
{ ... } # DO THINGS
```

OR

```
@app.middleware('http')
def inject_context(event, get_response):
try:
db=boto3.resource("dynamodb", region_name=AWS_REGION).Table(TABLE_NAME)
ctx = { "db": db }
event.set_context(ctx) # SOMETHING THAT ALLOWS ME TO ADD THINGS TO THE REQUEST
return get_response(event)
except (ResourceLoadException, ResourceNotExistsError) as err:
{ ... } # LOG AND RETURN 500 RESPONSE

@app.route("/list/things", methods=["GET"], content_types=["application/json"])
def run_get_account(event):
{ ... } # DO THINGS
```

For while I was setting some values globally and accessing them directly from the functions, but doing this creates other issues.

Start by reviewing the HTTP middleware flow, the get_response callback, and the Request object described in the issue. Determine whether middleware can add request context or whether handler signatures must change; done means documenting or implementing a supported way to pass the database client to route handlers while preserving error handling.

Written by the indexing model from the issue text.