Can I get a tourist visa in Vientiane just afters spending some time in Thailand on the visa exempt? There's some 6 month rule I cannot understand right because of a lack of logic in what the Thais wrote.

No problem.

Not such thing as 6 month rule.

Be aware that you can obtain a 30 day extension to your visa exempt entry and also to your tourist visa if required. 

 

If getting a tourist visa in Vientiane, and returning by land, there is not too much to worry about.

 

If you have applied for tourist visas in Vientiane before, there is a possibility that the application could be refused, but I imagine you are not in that situation. Even (worst case) if you were refused the tourist visa, you could still reliably enter visa exempt which, with the 30-day extension) gives you a couple of months to decide on next steps.

 

Only if you were in the situation of a realistic chance of a denied tourist visa in Vientiane and you had already received two visa exempt entries by land in 2022 do you standard any real risk.