If you were to write your first sentence, which I'm not sure that I would, which I'll get into in a moment, you would write it as follows:
"During my daily work, I’ve met many interesting people whom I was able to
connect with."
You need a comma after the word work. "During my daily work" is an introductory modifier. As it adverbially modifies have met and precedes the subject, you would follow it with a comma.
You also need to say "whom" after the word people. Why you may think you don't need to comes from the common mistake people make using who instead of whom. The word who as a pronoun can work like the word that. In English, when that is used as a pronoun in a restrictive clause, it can be implied, so omitted. When who is used to mean that, it can likewise be omitted. So, if you mistakenly think who is the right word for your sentence, you might think you can omit it. But who isn't the right word because who can't function as an object, only whom can, as in, "I've met many interesting people with whom I can connect." Not only is whom the object of the verb connect, but it's also the object of the preposition with.
The third problem with this is it's redundant. If you were saying "connected with" in its sense that would mean you had created a deep interpersonal connection with those people you met, then it wouldn't be redundant. However, based on your example, you're not saying this. You're using connected with in a very cursory way, essentially saying, "I met people I was able to meet.
Your second option is much better but should appear as follows:
During my daily work, I've been able to connect with many interesting
people.
In order to be grammatical, you would insert the necessary comma after the introductory modifier for the same reason explained before.