This may have something to do with your browser blocking Pop-ups and redirects!
To allow pop-ups and redirects, in chrome, go to Settings/Privacy and Security/Site Settings/Pop-ups and redirects then you can add apps.powerapps.com to the list of allowed sites for Pop-ups and redirects
I needed a similar function and this is what was preventing me. This will work properly if you allow Power Apps to open pop ups combined with the function:
Launch("google.com",{},LaunchTarget.New); Launch("bing.com",{},LaunchTarget.New)
When Power Apps first launches a website by default it opens a new tab. If you leave that tab open, any other launches from power apps will launch in the tab Power Apps has already opened. So when you launch multiple websites, it will technically launch all of them it will just land you on the last website in your chain of launch functions as it opens all of them in the same tab sequentially. That is why LaunchTarget.New is needed