If I change any mod config options in game and apply them, as soon as I get back to the game it pops up the "choose planet" menu even though I already did so hours ago. Picking the same planet I am already on spawns me, trapped, as a new character with my previous character also existing and preventing me from moving.

I cannot find a way to dismiss the choose planet screen if it incorrectly appears.

I ran into this same issue. A quick fix is to extract the mod from the zip file into folder format, and then comment out line 104 of planet-picker_0.4.2/control.lua by adding two dashes to the start of the line:

-- script.on_event(defines.events.on_runtime_mod_setting_changed, settings_changed)

This worked, let's hope it's not there for a good reason lol.

Thanks for the reports. This was meant to update the available planets to pick from when settings changed but was not taking into account that the UI was closed properly, and should now be fixed.