As a native French speaker, I would say:

J’ai écouté toute la journée l’audio que tu m’as envoyé

Thus I would use the passé composé tense.

If you would say j’ai écouté l’audio, then it would means, you listened it once. With the additional toute la journée, it means that you have been listening to it all day.

By the way, it sounds strange to talk about audio. I would use musique or an other word which describe which kind of audio you have been listening to.

Continuous tenses don’t have an exact equivalent in French. It may depend on the context, but most of the times we use just use the corresponding non-continuous tense.

I’ve been listening to the audio you sent all day : J’ai écouté l’audio que tu m’as envoyé toute la journée

I’ve been practicing : Je me suis entraîné

It’s not that simple though, continuous tenses will be translated in different ways depending on the situation and what you want to put the focus on.

For example, you can also use "j’ai passé [time period] à [verb]", or "ça fait [time period] que [verb]".

I’ve been working all day : J’ai passé la journée à travailler

I’ve been waiting for you for 2 hours! : Ça fait deux heures que je t’attends !

They convey different ideas, the first one is more focused on how you spent your time, and the second one on how long something was.

Also, "j’ai passé [time period] à [verb]" refers to an action that is already completed or that has just finished, whereas "ça fait" has to be about something that has just finished (like waiting for your friend) or something still ongoing :

J’ai passé 20 minutes à chercher mes clés : the action is over, so the speaker has found their keys.

Ça fait 20 minutes que je cherche mes clés ! : the action is not over, the speaker is still looking for their keys.

I liked your analysis of what you knew it was not. You know your tenses and conjugations. However, as we often do in assuming things too quickly, your very first assumption was wrong. Since you have been doing it and STILL ARE doing it, it IS the present tense. The form is present tense + depuis.
« J’écoute l’audio que tu m’as envoyé depuis toute la journée. » Voila