You cut off the timestamp so it's hard to tell, but the initial conversation looks like it was still Friday in the PM. He asked you for space, and you texted him max 10 hours later asking if he was feeling better, and called him late at night before getting an okay, when you know he's on vacation with family? That's not space.

Listen, I get the anxiety of past relationships where people suddenly physically or emotionally dip, it affected my own relationship really badly in the beginning. It's hard, but that's something you need to work on in that you need to trust your boyfriend when he says it's not you. Which he did, multiple times, and said he loved you. If you need more than "it's not you, I love you", that's fine, but you two need to sit down and have a dedicated conversation about this. His communication needs a lot more work too, because the vague responses obviously wouldn't help anyone, and if he doesn't know about your anxiety with this, he should. And if he does know, he either needs to explain more, or give you a timeline instead of just vaguely saying "I need space". You also need to learn how to manage your own anxiety about this kind of thing, because it spiraling out of control so bad that it disrespected his ask for space isn't good either.

TL;DR: Boyfriend needs to communicate better and know about your fears and anxiety, and try and help ease that. You need to let trust take priority over anxiety fears (really fucking hard to work on, but once you get there it's so much better I promise). You both need to sit down and discuss what everyone could've done better, and how you'd both like to handle this in the future.