Preliminaries: Latin is said to lack dedicated, grammaticalised particles such as "yes, no, OK, duh, meh, well..." used for confirming, negating, acknowledging or contesting entire sentences. This is true to some extent - even some Romance languages still lack single-particle answers to yes/no questions, e.g. European Portuguese; however it often entices blanket statements to the effect that Latin has no concise, single-word expressions that can be used as translation equivalents, and that the only option is repeating entire constituents (verbal or noun phrases, adjectives) - and this is not true. Not only did such expressions exist, more may well have existed but were never consigned to writing. In some cases those blanket statements can stray very far from the truth, as exemplified by another reply here. Relying on cookie-cutter, context-blind rules of the type "to say 'yes' repeat the verb" is a sure-fire way to produce non-sequitur replies that will bewilder your interlocutor - some examples can be found in this article on the acquisition of Portuguese. I've seen many of these from learners of Latin.
In a situation where a precise equivalent is lacking, it often pays to try and rephrase the concept very literally - this will usually give you some bordering concepts which do have equivalents in the target language. In this case what we're dealing is formulaic particles and interjections known as backchannels. These are highly language-specific, idiomatic, and often tricky to get your head around without a lot of exposure.
Here's some adverbial options that come to mind - I specifically focus on the most neutral, acknowledging "OK, fine, all right" and exclude expressions of permission and concession:
- bene habet! = "it is well, this is fine, all right, deal". This is the closest Latin has to an all-purpose acknowledging and affirmatory formula.
- bene( e)st is the more official version of the same, and bene is colloquial verging on abrupt; with an exclamatory intonation, it's elliptic for bene fēcistī, dīxistī etc.
- euge! was a trendy late republican Graecism, similar to how "OK" has been borrowed into many modern languages. Being emphatic, in your example it could be used to mean "all right! finally! :D" or "yeah, great -__-".
- bene fēcistī = "you did well, it's good/nice of you to have done this". Very neutral, and I suggest this in most cases where the former doesn't work for some reason.
- probē, rīte, jūstē, rēctē for a more rhetorical choice of adverb.
- bene factum! = "well done, nicely done". May sound a bit impersonal and insincere; better reserved for praising a good outcome ("nice!").
- rēctē (est) = "(it's) all right, all is proper". Signals that the speaker is fine with the situation; not so much a general particle of acknowledgemenet that is the English "right".
Here's some verbal ones:
- audiō = "I hear you". This is a general confirmatory verb that additionally expresses support for another's words and can be compared with the now severely restricted English "hear hear!".
- teneō = "I've grasped, taken on board what you've just said". This expresses a more active involvement than "OK" does, but is still a good choice for a general confirmatory backchannel, also among modern-day Active Latinists.
- intelligō "I discern your meaning, I understand, I see". While an obvious first choice, it's likewise obviously pondering and therefore less suitable as a thoughtless reply.
- probō! = "I approve, you have my approval". This doesn't sound nearly as official and overbearing in Latin as it does in English; quite the contrary, it verges towards "good man!".
- laudō! "you have my praise" is the more official, but still not overbearing option - more like It. complimenti.
As you can see, even just focussing on the most neutral meaning of "OK" nets you a great number of various expressions, with the caveat that none of them is as conventionalised and devoid of meaning as the English interjection. Another leitmotif is that the Latin often seems fairly literalistic and direct - this isn't a result of literal translation from English, such directness is a pervasive feature of Latin.
This is how statements like "there's no single word for it" should really be interpreted - that there's no context-independent way to express acknowledgement, which means you'll have to master a whole bunch of different strategies. Again, most of the time this will require a lot of exposure, and one has to be careful about using expressions one hasn't mastered in contexts where one hasn't met them yet - at the very least I suggest checking L&S or Forcellini, ideally a corpus like PHI; not incidentally these are great places to gain exposure in context, especially when used in conjunction.
- Martins, Ana. (2006). Emphatic Affirmation and Polarity: Contrasting European Portuguese with Brazilian Portuguese, Spanish, Catalan and Galician.
- Santos, Ana. (2003). The acquisition of answers to yes – no questions in European Portuguese: syntactic, discourse and pragmatic factors.