How can I adapt my scientific writing for the modern web?
For journals, at least, many now publish online in HTML.  This includes many large cross-field publications including well-known venues such as Nature and PLOS ONE,
to name only a few of many.  Your paper will generally be available in PDF as well, but the default that the journal steers people to is generally HTML.

An action you might then take would be to choose to submit only to journals with HTML publication of this sort.