After making a new Steam Family before the old system gets shut down, it no longer shows the playtime of owned games that were played before joining a family on the Steam App in the Library section. This also applies to the Recent tab as well. Just to note that playtime/recent game tracking does work with anything played after the Steam Family creation date, just not for any game played before that date.

I am unsure if this is "working as intended" as it would show both overall playtime and any games played before through the old Family Sharing system. This only happens within the Steam Mobile App and is not reflected the same on my profile or through any website.