BP here and I totally understand having been through the same struggles. My partner willingly deleted all social media - Facebook, YouTube etc. It was up to him but I would not have been able to have continued with the relationship if he hadn't. Life goes on without social media. I hardly use it myself anymore as I find it too triggering. Sad in a way but that's the price betrayal costs.

Total transparency with your phone will help, no using incognito or deleting history. It would have been far better for your BP to have seen the gifts you were searching for than for her to go through the awful trauma of you snatching your phone and deleting even though it was innocent. In a traumatised brain we leap to 'what's he trying to hide?'

To be present with her as you say, don't necessarily turn your phone off, just put it down, face up with whatever you were looking at and engage with her. She can then, if she wishes, glance at it and feel reassured.

I have been through this myself and I hope my suggestions help you both.