After the FFXIV 5.1 patch the new launcher gets “stuck” at the top of the scrolly page with Mogry Kiosk banner. It takes up to 3-5 minutes to “auto scroll down” to the login prompt. After entering login information, it takes another 3-5 minutes for the “Play FFXIV DirectX 11” to pop up. Once the game launches, it’s smooth as butter.
At least, the new launcher opens for you.
I went back to the old launcher to avoid problems. However, I’m not using Lutris but Proton for FFXIV. So I’m not sure if this works for you as well.