Username checks out. Hmm Zwiebeln!

yogurt with a sprinkle of random veggies

Don't let Greeks or Turks hear that.

You need yoghurt, the heavy stuff with 10% fat, olive oil, garlic, cucumber, pepper, and salt. Nothing else. No, no dill, no mint (WTF?), no nothing.

Julienne the cucumber. Very fine is better than fine as long as you're not producing mush. Salt it, let it stand for 10 minutes, then squeeze dry, toss the water. Add yoghurt, should be about two to three parts of yoghurt for one part cucumbers, by volume, don't sweat it. Take about a clove for 500g of yoghurt (that's a clove, not a bulb, yes it's quite little, but it's raw and it's going to infuse), surgically remove the sprout (that's where the nasty stuff is in garlic), chop finely. I said chop, not squeeze, yes it makes a difference. Add with pepper and salt and some olive oil, put in the fridge for at least one hour better a day, well covered (closed container is good, cling film if you have to), mix again and do final taste and consistency adjustment with pepper, salt and olive oil. Pepper should be subtle AF, supporting the garlic, not supplanting it.

...it's absolutely fine to do other yoghurt sauces and in fact in Germany you'll see three or four at any Döner shop, but don't call the non-tsasiki tsatsiki, please. If you want a herb sauce, call it herb sauce. There's no herbs in tsatsiki. (Sauces differ regionally in Germany -- there's always going to be tsatsiki, around here you also generally get curry, hot or mild, as well as cocktail sauce (no, not mayo based, it's still yoghurt)).

I make tzatziki, an that, it is not.