Chemistry - Cleaning with vinegar and sodium bicarbonate
Solution 1:
Your intuition is on point. Pretty much all the "lifehacks" praising cleaning abilities of vinegar and sodium bicarbonate are ineffective. The reaction appears vigorous due to the formation of carbon dioxide gas, but what is left is a diluted solution of sodium acetate:
$$\ce{CH3COOH(aq) + NaHCO3(aq) -> NaCH3COO(aq) + H2O(l) + CO2(g)}$$
Sodium acetate doesn't have any pronounced cleaning abilities. It doesn't act like a surfactant, doesn't drastically increase solubility of the impurities, or participate in complexation helping to dissolve metal-containing compounds.
As for unclogging abilities—yes, this is something that my grandmother used to use, but these days there are much better alternatives. The idea was to pour some hot water into the system and then put a couple of spoons of baking soda into the drain creating warm concentrated solution in the siphon. This solution would also be mildly basic due to hydrolysis and help to dissolve some fat and thin hair:
$$\ce{HCO3^-(aq) + H2O(l) <=> H2CO3(aq) + OH-(aq)}$$
After some time (approx. 30 min) it would make sense to add some vinegar hoping the reaction would cause mixing up the constituents of the clog and excessive pressure would help to push the waste further down the drain.
Solution 2:
Better is using washing soda alone first ( instead of baking soda ), pouredby boiling water and kept there overnight. Next day vinegar may be used to make some bubbles desintegrating the clogging.
Washing soda has cleaning ability by itself and has better solubility than baking soda. Adding vinegar later is not to produce some extra powerful chemical cleaner, but it's effect is mechanical. It is producing CO2 bubbles and pressure to tear and push clogging, hopefully weakened by prior soda action.
Detergents then make the clog desintegration easier.
An even stronger cleaner is sodium hydroxide, that is often used as well. But is cannot be used alone, without soda, to produce CO2 with vinegar.
Note that majority of clogging is caused by protein a/o fat rich materials, like hairs, that are chemically dissolved in alkaline solutions.