Learn Finnish: Mulla on varaa ostaa tällaista luksusta. - I can afford to buy this kind of luxury.

This is part of a specific Finnish structure for expressing capability. When you have the resources to do something, you use the possessive structure (mulla on) followed by the abstract resource in the partitive case. Here, varaa means having the financial means. You use the exact same pattern for having the time (mulla on aikaa) or the energy (mulla on voimaa) to do something.

How does the noun varaa connect to verbs like varata (to book/reserve)?

They share the same root! The base noun vara essentially means a "reserve", "provision", or "wealth". So having varaa literally means having the "reserves" (usually money) to do an action. The verb varata comes from this same idea of securing or setting a reserve aside.

The verb ostaa normally takes a total object (like ostan auton). Why are tällaista luksusta in the partitive?

Because luksus (luxury) is being treated as an uncountable, abstract mass noun here. You are buying "some of this kind of luxury" rather than a single, countable item. If you were talking about a specific luxury item, you would use the total object, for example: mulla on varaa ostaa tällainen luksusauto (I can afford to buy a luxury car like this).

How do I attach the action I want to afford to the phrase mulla on varaa?