** IF YOU INSTALLED THE GAME INTO THE NON-DEFAULT LOCATION - THIS MAY WORK FOR YOU **
I was having this similar issue -- starting about 2 weeks ago. I had found a work around (by editing the Leagueclientsettings.yaml after each time I closed the client). However, today that stopped working.
I did get the issue resolved, however, by making sure I installed the game into a "Riot Games" folder. I noticed this difference on a friends working installation.
I have had my installation in "G:\Games\League of Legends" since the release a decade ago. However, it looks like with the 10th year anniversary Riot is switching up where the launcher lives (in a "Riot Client" folder inside the "Riot Games" folder).
So I switched my installation folder to "G:\Games\Riot Games\League of Legends" ... and behold! It all patched up nicely. I did have to close and restart the launcher once (The "Play" button wouldn't do anything) -- but after that, it has worked 100%.
Hopefully this helps you!