Roamit can do that, and it does very well. It's available in the Microsoft Store for PC, Xbox and Windows Mobile, in the play store for android, and in firefox addons/chrome web store as an addon for your brower. It can send text, link, automatically sync clipboard, and link with Windows Timeline.
As explained in Roamit Privacy Policy, the app doesn't store any of your clipboard stuff on its servers. After server receives a request from a client containing clipboard data, it just sends several requests to Microsoft Graph REST API (for Windows devices) and Google Play notification service (for Android devices), and does not store any clipboard content at all.