Well, I don't put that stuff in a jersey, it would drive me nuts.
I use a Road Runner Burrito bar bag. I store my iPhone in there, a multi-tool, and a small zippered neoprene wallet. I can also fit in an energy bar or two. I don't need to carry a tube, but if I did, I think I could probably fit that in as well. If not, they have a larger version called the Burrito Supreme. Personally, I prefer a small saddle bag, but Bluetooth doesn't work as well with the phone in a saddlebag. The bar bag doesn't look great (I'm talking aesthetically, the bag itself looks fine), but it works.
https://roadrunnerbags.us/collection...-handlebar-bag
A bottle cage tool kit/keg is another option. Or maybe a Topeak Cage Pack. It's designed for a bottle cage, but it looks like it might also fit a jersey pocket, though I'd imagine it would be less bulky to just cram stuff in the various pockets.
https://www.topeak.com/global/en/pro...g/796-cagepack