Mashup engines were so gloriously hopeful.
It feels like Opera browser was super early (as usual), with widgets (2008). Eventually we had a widget spec (2013). Overall PWAs cover a lot of this terrain today as a packagable standalone webapp, but also there was a lot more excitement in the world about small UI programs that overlayed and/or worked with your desktop at large, that we don't see today (but omgosh I wish Project Fugu had browbeaten Android into having a capable web home screen widget option!) https://www.wired.com/2008/05/opera-targets-widget-developer... https://www.w3.org/TR/widgets-apis/
But more than widgets, there were such interesting attempts ongoing to stitch together an inter-site inter-networked web. Google Buzz's protocols & especially the Digital Salmon protocol (2010) was a fore-runner to Mastadon, a way for discrete digital identities to push Atom/RSS like entries (such as a "like" or comment) at each other. Trying to work under the Open Web Foundation (OWF). http://blog.jclark.com/2010/02/tour-of-open-standards-used-b... https://news.ycombinator.com/item?id=1140893
Even before this, the OpenSocial folks were working on very ambitious cross-site data and widget systems. I really think some deep-diving technical retrospectives into OpenSocial would be incredible, could maybe help us shake loose some of the rut we're in with uncomposeable consumeristic computing being the only thing we can even think to do. https://en.wikipedia.org/wiki/OpenSocial