Just having a trace of your route probably isn't very useful in a lot of cases, since it's going to be mostly on roads that are already mapped. Instead, you'd probably want to map the actual paths, in which case you can view your GPS trace in the editor to map from without having to share it publicly.

The Strava heatmap is also licensed for usage in OSM, and in a lot of areas it has pretty good coverage of bike paths already (https://wiki.openstreetmap.org/wiki/Strava).

How many bike paths have been added to OSM as a result of the Strava heatmap identifying them?

I don't think there's any exact numbers. You can search for changesets that have Strava listed as a source [1], but that doesn't mean the Strava data was actually used.

[1] https://osmcha.org/?filters={"source"%3A[{"label"%3A"strava"...}

Thanks! Note that the link doesn't seem to work at all for me :( But I'm happy to see that someone is drawing the connections from the data somehow.

There should be an extra } at the end of the link; HN seems to be interpreting it as a separate character for some reason.

I've got OSMTracker which I think might be what you're looking for.