So, in English, we don't distinguish 1-time events that have just been completed and 1-time events further in the past. Translating it into the present perfect doesn't solve this problem, because that too, in English, can refer to an event far in the past. So, my question is, wouldn't "I (just) drank (the/a) beer" be an adequate translation for this as well? Since English doesn't distinguish the same factor, I think both work here. If I'm wrong, can someone explain?
-me- is the perfect tense. It indicates that the verb happened and completed resulting in the current state of things. Just like "have" in English. So "nimekunywa bia" - "I have drunk beer" as opposed to "Nilikunywa bia" - "I drank beer".
Here's a better example: "Nilianguka" - "I fell" (but then I got up) vs. "Nimeanguka" - "I have fallen" (and am still on the ground).
The tips & notes do a poor job of explaining this and I was surprised to read the explanation about it being a recently completed event or an event further in the past. That's not correct. I think it was an attempt at explaining perfect tense in simple terms. Anyway -me- is perfect tense and -li- is simple past tense.
I am curious about the "recent" aspect being correct. I previously studied another Bantu language, Tonga, and it had tense markers that indicated recently happened (li - I think) versus happened a long time ago (aka), which were different than just perfect past and past tense.
This video lesson shows the use of "me" with a sentence using the perfect tense and adding "just" with the Swahili words "sasa hivi" (just now), also there are other uses of "me", for example for "used to" sentences or with expressions with "being late" and "being tired".
Amekula sasa hivi. = He/She has just eaten.
This other video lesson shows the use of "me" with statives:
Umelewa. = You are drunk.
So, I think we can find other uses of the tense particle "me" and sometimes we would need to add an adverb to express recent actions. I hope it helps. ;)