After creating a Lightfoot Halfling Ranger when going back to edit the character i am presentet with other 2nd level fighting style options, which i wasn't abel to choose before

they are: Blind Fighting , Druidic Warrior and Thrown Weapon Fighting

taking Druidic Warrior allowed me to choose 2 cantrips, which did appere on the character sheet and are usable

this seems to be a bug

Those are from the Optional Class Features added by Tasha's Cauldron of Everything. If you recently ticked the box for Fighting Style Options in the Optional Features Manager under the Ranger Class, that's what gave you the new options.

I did in fact not enable Optional Features for this character, nor do i own Tasha's Cauldron of Everything

Ahh, I just tested on a character without Optional Features, and you're right, it still shows those options.

I think this is a known issue? At least I recall it being mentioned on the forum before.

I'm looking for a way to purchase the individual fighting styles without purchasing the entire book. Is this just not available at this time?

You can't purchase fighting styles at this time