deeplinks.js uses the Selection API, the TreeWalker API, and ES6 modules with dynamic imports. This is supported by around 94% of browsers in 2021, according to caniuse, including modern (2019 and later) versions of Chrome, Firefox, Safari, Edge, Opera, Samsung Internet, and QQ Browser (including mobile versions, where applicable). The most widely used unsupported browsers are Opera Mini (1.09% global share), UC Browser (0.98%), Internet Explorer (0.87%), and KaiOS Browser (0.06%). Note that while Opera Mini is unsupported, that's different from Opera Mobile, which should work fine — Opera Mini is well-understood to break many things that are dependent on Javascript.
The end-to-end test suite is currently run on Chrome and Firefox, but bugs will be fixed for any browsers that have support for the necessary APIs.
Multi-select works on supported browsers (I think this means only Firefox, but possibly other browsers as well). Trying to open a multi-selected link on a browser that does not have multi-select support will result in a error message, and only the first selection being selected.