New Relationship Anxiety - Support Appreciated

Hello, I’m diagnosed with social anxiety along with depression and BPD. I’m very high functioning and seek regular therapy so I’m managing (these days it’s challenging but I’m still breathing). I recently started a new relationship (almost two months in now) with a very lovely person. He just came out with anxiety a few days ago to me. He’s going through unemployment and been dealing with a difficult potential employer in a series of interviews. He had one interview on Sunday and one today (was supposed to be yesterday but got rescheduled). He tells me upfront that he’s anxious so I’ve been checking in with him daily over text - just telling him I’m here/wishing good luck on interviews, etc. Personally, when I’m anxious I shut down for a few days but I really appreciate when people reach out. But I don’t know how anxiety manifests for him. So, after sending him check in texts for four days in a row (he replied very quickly to all of them but has not initiated contact these four days), I’m starting to worry that I’m intruding. (I also only send one to two texts per day). Now my social anxiety is triggered and I’m worried that I might come off as clingy or scare him off. I just want to be supportive but don’t know how to do it. Any thoughts, tips, advice? Thank you so much!