Hey Ojlom, you can currently find the "Compose" page in two places that I know of. The first as described above. The new app design is providing one exercise summary below exercise days on the Today page. Tap on it to view the summary. When you view your exercise summary, there are three buttons at the top right of the page. A box with arrow point up, a pencil, and three dots. Tap on the box with up arrow and the "Compose" page will pop up with all your historic data. This includes all exercise sessions, food, sleep, etc. in the old format. This is where the heart rate graphs are, or the sleep graphs and menus as well as other historic data about your activities. The reason it's called "Compose" is because you can distribute these data by email or messenger or however you choose. Try choosing "Next"... and then "Share". All your communication options are listed.
Another way to find this page is to go to the "You" section of the app. Under the Community header, scroll one to the left and find the Feed tile, (cell phones are too narrow to display the four tiles) tap and a page opens asking you "What are you up to?" with a runner, a moon and a camera. Tap on any one of the icons and the "Compose" page will appear with 8 tiles including Sleep. You can also review your badges from there too. This is where all your historic data is hidden by Google or forgotten by Google and therefore not removed. There should be a button on the front page of the iOS app to make this data more accessible.
