It's a judgement call. You can certainly combine dialogue and actions in the same paragraph, and it's generally a good idea to do so when writing about someone giving a speech. But as you said, the "wall of text" is also a potential problem.
The speech your character is giving will probably have separate ideas in it, times when you would make a paragraph break if you were transcribing the speech. That's likely a good place to make the break in your action/dialogue.
The family was all staring at me, all waiting for me to start making
sense. I did my best. "I know it's been a long time. I know it's been
hard to figure out what I've been up to, and I'm sorry if that's been
I took a deep breath. It was hard to argue with an introduction that
general, but I was about to get into the meat of it all, and that's
where the trouble would come. "The thing is, I've been doing some
digging. Some research, and what I've found has changed my mind about
so much. First of all," I said, fixing my gaze on Charlie, "I found
out about that night. The night you and Alexandra made the deal."
Alexandra and Charlie exchanged shocked looks and Charlie started to
sputter out a denial, but I held up my hand and, miraculously, he
complied with my request for silence. I guess I must have really
caught him by surprise.
"And I know about everything you did after that, all the ways the deal
played out..." etc.
Might not make sense without the context, but I think it shows the general idea? Mixing dialogue and actions in the same paragraph is good, but it's also good to avoid walls of text by using logical paragraph breaks.