If you like it really simple without sharing but don’t want to use an app, you can use these progressive web apps that run in the browser. They keep the state in the same browser, so you should create your shopping list on your mobile phone, if you will take that phone shopping with you:
- https://angry-swanson-d3210d.netlify.com/ from https://github.com/Kacperell/Shopping-list-PWA
- https://shoppinglist.schmuckli.dev from https://appsco.pe/app/shoppinglist
If you would like to save the state on a server of yours, openHAB (and also Home Assistant) are not made for this Job. Managing and syncing a list has nothing to do with the automation or control of smart home devices. There is a reddit thread over at r/selfhosted: https://www.reddit.com/r/selfhosted/comments/7djg9r/google_keep_selfhosted_for_shopping_lists/ They discussed self-hosted, todo-list/shopping-list-like apps for running yourself.
EDIT: also https://www.rosehosting.com/blog/self-hosted-alternatives/#evernote
I hope that helps you on your journey 