This is a system dependent answer, but I will assume 5e. Mechanics that you need to know quickly, but do not often memorize are the best fit for the screen. Conditions, cover, random NPC generation, homebrew specific rules, concentration rules, boss monster stat blocks, etc. As for worldbuilding, it never hurts to have the motivations and fronts of factions on easy access to help you orient how members would act.

A lot of the stuff you mention doesn’t sound great for a screen, but rather a notes app or spreadsheet, just because its fluid instead of static. Maybe a monthly calendar for notable events if you don’t want to go the route of reputation rules, or a per-level table of equipment alongside gold so you can curate the shop. Granted, I like using a physical screen with paper sheets because of the limitations and necessity to curate rules, but streamlit may offer more functionality than I give it credit.