since the sentence says “for” the last couple of days you should say I have been meeting. But in a real conversation it would sound more natural to say “over the last couple of days” and then you could say I have met or I have been meeting. In conversation if you wanted to emphasise the point that you had the experience of meeting these people you would say “I have been meeting a lot of interesting people for the last couple of days”. If you wanted to emphasise the people that you’ve met and continue to discuss some of these people you would highlight this emphasis using the sentence “ I have met a lot of interesting people for the last couple of days.”

"The last couple of days" is a time period extending to the present. British English uses the present perfect in this case. American English uses the present perfect or the simple past in this case. https://www.ef.com/ca/english-resources/english-grammar/present-perfect-vs-simple-past/