I am not certain why you are getting only timestamps, maybe a problem with how you look at your data? There is a way to make tags into fields which is not that well documented but even with it you should still have some tags attached to all metrics.
But you can attach more:
For http requests (including data_received metric from those) you can add tags with the
k6/http's method using params. It is important to note that for the http.get, there is no body argument, so the
params are the second, not the third, argument as with the others.
If you are using websockets, see their documentation.
I suppose you can use a custom metric and are add some values if the built-in are not enough. If you take a look at the k6/metrics documentation and more specifically the example you will see that each and every time you add a data point you can add a tag for that datapoint, not the whole metric.
Additionally you can output to json with
--out json or
--out json=file.json and than use jq as shown, again in the documentation.