I'm not the original creator of the issue but I've started experiencing the same problem in the last 10 days and it's been very annoying so I'll respond in the requested format in their place (if I should make a separate issue instead, let me know)
Steps to Reproduce:
delete/rename existing launcher_profiles.json
launch the launcher so it generates the launcher_profiles.json from scratch
create a custom profile and start up the game using that profile
close the game and open the launcher again or look directly at the launcher_profiles.json
Observed Results:
The order of Latest played shows the order as it was before launching the custom profile (Latest release profile above the custom profile), and the lastUsed value of the custom profile within launcher_profiles.json remains the default 1970-01-01T00:00:00.000Z
Expected Results:
The custom profile should display as the most recent played profile (custom profile above the Latest release profile), and the lastUsed value of the custom profile within launcher_profiles.json should be the time the profile was last played
see this screenshot for what the result is when I follow the steps I mentioned in Steps to Reproduce:
However when using the setting Keep the Launcher open while games are running, like Dylan said in his edit, the launcher_profiles.json does update the custom profile's lastUsed. In which case the steps to reproduce that behavior are the following:
delete/rename existing launcher_profiles.json
launch the launcher so it generates the launcher_profiles.json from scratch
enable the setting Keep the Launcher open while games are running
create a custom profile and start up the game using that profile
close the game and optionally close the launcher
open the launcher again or look directly at the launcher_profiles.json
Which results in the following screenshot:
It should be noted however that this only bypasses the issue whilst the Keep the Launcher open while games are running setting is enabled, Disabling it afterwards makes it so that any lastUsed in launcher_profiles.json is not updated again from that point on
Having re-followed the steps I've previously describe in both the current release (launcher v3.3.13-2.1.3) and in beta (launcher b.3.3.13-2.1.3) it's still unresolved for me
In case it somehow helps with locating the issue: the Date Modified on the launcher_profiles.json file itself does get updated when launching a profile