That's an incorrect characterization.
Heaviside is pre-Michelson-Morley. Einstein is post.
The fact that "Ether doesn't exist. Electromagnetic waves simply transmit without a medium." is a VERY VERY VERY big change in the fundamentals of physics.
That opened the door for the hypothesis that "all physical laws look the same in all inertial frames" because without "Ether" you cannot anoint a preferred inertial frame. The Michelson-Morley experiment was the first test of that hypothesis.
And, to be fair, the kind of fields interpretation that Einstein championed has weaknesses:
1) It's an absolute bear to compute--the Heaviside-Hertz formulations lend themselves to engineering much better pre-computers.
2) It had severe experimental holes--at the time.
For example, the Einstein fields interpretation makes the prediction that an an excited electron in an atom will never decay. That, of course, was nonsense--excited atoms always decay to ground state. Except--now that we can isolate single atoms we absolutely see that single atoms don't decay--only the ensemble interactions cause them to decay.
I just read the 1893 preface to his Electromagnetic theory vol 1 linked in another comment. It mentions the Michelson and other experiments and talks about how to accommodate them (in now-unfamiliar terms I don't understand).
And, even if Einstein didn't know about it, people who read Einstein's paper did. That meant that Einstein's paper fell onto fertile soil rather than simply being a mathematical curiosity waiting to be discovered at a later time.
Whilst CliffStoll's quote (and link) is from Paul J. Nahin's article in the Royal Society journal it's also worth highlighting the fact that Nahin has written a full bio on Heaviside (it's mentioned in the article's footnotes but might be overlooked). I have a copy of the book, it is excellent, it's likely the most comprehensive and authoritative written on Heaviside, and I'd thoroughly recommend it: Oliver Heaviside–The Life, Work, & Times of an Electrical Genius of the Victorian Age; Paul J. Nahin PJ ©1988-IEEE ©2002-John Hopkins Uni, ISBN 0-8018-6909-9 paperback ed.
It's all very well to praise Heaviside but if one really wants to get a feel for the extent and depth of his work then I refer one to the following works of his that are on the Internet Archive (they're out of copyright so they can be downloaded). Note, as with many works, the Internet Archive has multiple copies some of which are more readable (or better scanned) than others, so the seemingly multiple entries are not duplicates. Two other points to note, this list is not comprehensive and the IA's file-naming conventions are sometimes skewed or confusing (apologies if I've made any typos):
Electromagnetic Theory, Volume-1, Heaviside, Oliver, 1850-1925, 1893 edition: https://archive.org/details/electromagnetic00heavgoog
Electromagnetic Theory, Volume-1, Heaviside, Oliver, 1850-1925, 1894/1912 ed.: https://archive.org/details/electromagnetict01heavrich
Electromagnetic Theory, Volume-2, Heaviside, Oliver, 1850-1925, 1894/1912 ed.: https://archive.org/details/electromagnetict02heavrich
Electromagnetic Theory, Volume-3, Heaviside, Oliver, 1850-1925, 1893 ed.: https://archive.org/details/electromagnetict03heavuoft
Electrical Papers, Volume-1, Heaviside, Oliver, 1850-1925, 1892 ed.: https://archive.org/details/electricalpapers01heavuoft
Electrical Papers, Volume-2, Heaviside, Oliver, 1850-1925, 1894 ed.: https://archive.org/details/electricalpaper01heavgoog
Electrical Papers, Volume-2, Heaviside, Oliver, 1850-1925, 1894 ed.: https://archive.org/details/electricalpapers02heavrich
Electromagnetic Waves, Heaviside, Oliver, 1850-1925, 1889 ed.: https://archive.org/details/electromagnetic01heavgoog
BTW, a factoid just occurred to me that some may not know, which is that the earth's ionosphere—those ionized layers ≈100-200km above ground that reflect radio waves—is called the Heaviside layer: https://en.wikipedia.org/wiki/Kennelly%E2%80%93Heaviside_lay....
...And now some trivia straight from the almost-completely-useless information dept: somewhat strangely, the Heaviside Layer features in the musical Cats. It's at the point where Macavity the Mystery Cat tries to escape to the Heaviside Layer: https://blog.sciencemuseum.org.uk/cats-and-the-heaviside-lay... https://www.themarysue.com/cats-heaviside-layer-real/
"Up, up, up past the Russell Hotel
Up, up, up, up to the Heaviside layer
Up, up, up past the Russell Hotel
Up, up, up, up to the Heaviside layer"
https://www.youtube.com/watch?v=pKH63cRJ3p4
Methinks, Heaviside would not have approved (but then, that's rather presumptuous of me).
Unmentioned is his stumble in relativity theory: As Paul Nahin wrote,
Despite the ‘Einsteinian look’ of Heaviside's speed-dependent terms, his analysis was greatly lacking when compared with Einstein's. Heaviside started with moving charged matter and then applied some heavy mathematics to Maxwell's electrodynamics, while Einstein used nothing but the fundamental ideas of space and time, some simple algebra, and the two relativity principles (all physical laws look the same in all inertial frames, and observers in different inertial frames will measure the same value for the speed of light). Einstein's analysis is free of any special assumptions concerning electricity in particular and the nature of matter in general: to put it bluntly, Einstein saw the whole forest, while Heaviside and Thomson were looking through a magnifying glass at the bark on a single tree.
https://royalsocietypublishing.org/doi/10.1098/rsta.2017.044...