I don't know any app/software in this area.
If the user is the only user of the program, if there are no update of notes somewhere after publishing them on too different devices before synchronisation, perhaps you can use a local server on your desktop computer and apps that synchronize (or send notes) to it ?
AppTethering components could help on a local network (home or office).
MQTT is a solution : you send something in a queue an all "client" programs read what is in the list, but you should encrypt the content is you use something public.
Perhaps a Firebase (or other cloud thing) database can be a solution too.
If you already have a website (I'm sure you have), you can also try something like my "Planning API" project ?
- a web API server : a list of simple PHP script with no database to manage the CRUD operation, storing datas as JSON files in a subdirectory, change API keys and put it on a website (in a "complex" directory name)
- a Delphi FMX client app : it gets the datas from the server on startup, display them and send the changes to it by clicking a "synchronize" button.
In this project, all datas are stored on the server. A web connection is needed, but you can change the client app to have a "add note" feature without Internet and send them by clicking the button when a connexion is available.
https://github.com/DeveloppeurPascal/Planning-API
On the "liste de courses" project I have a real synchronization process and API : a web server (PHP and WebBroker available), a client app (Delphi FMX) which store datas locally and synchronize only changes. Each device have all datas, stored in a SQLite local database. The synchronization API works with a "changed level" on each record.
The current program store a true/false, an integer and a label. You can edit the code to store only a text if you want. The server can be published on a web site (for the PHP), on a server (Internet or local) (with WebBroker) or simply on your desktop. Synchronization can be done manually like it's coded or with a timer.
https://github.com/DeveloppeurPascal/Liste-de-courses
I think the "liste de courses" project is the best start to adapt something if you try to code your need.