Can I travel to Laos from Thailand using a land border and get a Tourist visa for Thailand while holding a South African passport?

That would be NO, you cannot enter Lao by the land borders, and you cannot even FLY in to Vientane unless you're in a booked tour group of 5 or more people.

You wanna go get a tourist visa you FLY to either Phnom Penh Cambodia or Singapore, OR Kuala Lumpur Malaysia, or either Ho Chi Minh City or Hanoi in Vietnam,

Those are the countries that are open (with easy entry requirements).

AT this time NO land borders are open to get out of thailand by, you can ENTER the country from Malaysia at Sadao or from Lao at Nong Khai

You need to look at the thai consulate you're going to go to and see what the requirements are and if S/A passports are on the list that take longer to process or not

You certainly got your work cut out for you 😕 🙁

Good luck