I attended a majlis one of the nights of Ashurah, and I was deeply touched by the story and what I had heard. I am a bit familiar with the basic Shia aqaid, and Alhamdulilah I did recently take the step to become Shia as I was originally a Sunni. My question is should we view the tragedy of Karbala moreso as a praise of the Ahlul Bayt or should we view it in terms of its broader messages (such as justice and imaan and oppression) without so much focus on the Ahlul Bayt? My understanding of Karbala was not with a focus on the ahlul bayt, but of the universal ideas of divine justice and truth. Also how much should we use the wasila of the Ahlul Bayt in dua?

May Allah (swt) bless you for discovering and following the truth
We should remember Ashura both in terms of the values and universal lessons but also because God commands us to love and follow Ahlulbayt in the Quran. Both are important

As for seeking intercession, again the Quran instructs this (5:35) so it is totally fine and islamically encouraged so use it as much as you can