These other actions you speak of such as reading etc. can be resting (though be weary of phone time as it may not be conducive to going back to sleep but that’s not a sin matter just a matter of health). Jesus had plenty to say about resting Matt 11 : 28-30 and he himself often went off away from the disciples to pray alone to God. One of the commandments bids us to have a day of rest and keep the Sabbath Holy, as God rested on that day. Rest allows us to renew and revitalise and so work better for God. I think this is even more important for those of us with sleep issues. Rest in the Lord , ask him to help you and accept his will for you, whether it be sleep or wakefulness. I’d suggest starting off this time with prayer and offering the time to him and then seeing how he directs you to fill the time. Perhaps you could prepare a few things to have to hand that might help you if you wish to go back to sleep/ or go to sleep in the first place or are resigned to getting up. I would not worry about being constantly productive, resting is essential
God bless you insomnia is not nice.