"I have been waiting for you for a long time."
"Topic-comment" is description that can be applied to a lot of Chinese sentences, including this one. The effect is to say "I, waiting for you, [have] waited...", or "(Regarding the topic of) I-wait-for-you, (the point to be made is that I) [have] waited..."
Where there's a verb-object compound followed by a complement of duration etc., the common sentence pattern is v-o + v + 了 + complement.
Without the second "了", I would read it as "I waited for you for a long time". With the second "了", I read it as "I've (already) been waiting for you for a long time (and am still waiting)".
There are a number of things going on.
One is that the double 了 structure requires the first 了 to immediately follow the verb. That's why the verb is repeated here, to get the object out of the way. You have the first 了 in the wrong place.
Another is that "认识" is a two syllable verb, and doesn't sound as good with the structure Duo is presenting here.
"认识" is also a stative verb, not a dynamic one like "等" (at least as these terms are applied to their English counterparts, "know" and "wait"), so it doesn't necessarily make as much sense to use verb 了, which is also known as "completed-action 了", as a stative verb can't be "completed" in the same way (but I defer to native Chinese speakers especially on this point).
In any event, I don't think the first 了 (i.e. the "等了") is strictly necessary here. (As a topic-comment sentence it becomes simpler without it — see my comment above.)
Shows a continuous action. Without it, it would just mean "I waited for you for a long time" vs this sentence means "I have been waiting for you for a long time"
See another of my comments on this page (the part about topic-comment sentences), and also take a look at these discussions:
I feel the last one is not really optional. Without it maybe the sentence will seem like a general statement that I often seem to wait for you a long time, or that I am willing to wait for you a long time, or that you can take your time because I will wait for you a long time. If we want to indicate that I have just been waiting for you a long time, we need the 了 on the end.
I generally agree. A question should be answered, or left for someone else to answer, and a downvote is a poor substitute for an answer — except where a question is clearly nonsensical and unanswerable, and getting in the way of legitimate language questions, or is relevant but has already been asked and answered several times, in which case downvoting helps to move new clutter down or off the page.
But for some repetitive questions it could indicate that an explanation needs to be inserted higher up on the page, where it can be easily seen by new visitors, which can be difficult, e.g. when the the top comment chain is an irrelevant pile-on of "me too" comments with hundreds of upvotes.