What leaves the storefront
Everything the app shows. Because nothing was written into your theme files, uninstalling removes the app embed and any app blocks with it, and there is no code to hunt down in your theme afterwards.
Billing and data
Uninstalling ends the app subscription, so no new charge is created. After an uninstall, Shopify sends the app a shop redaction request, and that deletes all of your store data: timers, counts, image records, and subscription records. Background images you uploaded stay in your own Shopify Files, because they were always yours.
If you install again later, the app reads your plan from Shopify, so you start on Free unless you subscribe again. The 7 day trial only applies to the first paid subscription a store takes.
Email timers already sent
Email timer images are served by the app. After an uninstall, expect those images to stop working in emails you have already sent, including automated flows. Take the snippet out of any running flow or campaign before you uninstall.