To put a real fine point on it … Your transmission was expected to last 185,000 miles. It’s now going to last 184,996 miles. Not keeping up with fluid levels & change intervals will do far more to lessen the life than an occasional grind.
That’s true of forward speeds, and perhaps a few oddball reverse designs. Most manuals trannys, though, engage reverse by moving an idler gear into mesh with the countershaft reverse gear and the output shaft reverse gear, with no collar or dog teeth. In this design, it is the actual gear teeth that grind into each other. Still, as long as the attempt didn’t actually break a gear tooth, which is usually pretty darn obvious, the extra wear is likely to be inconsequential.
These comments are all true with respect to automatic transmissions, but do not apply to manuals.
I’m guessing manual transmissions might fail from excessive grinding once in a while, but in my experience the rest of the car wears out before the transmissions. Reverse may be a little harder on the gears, but I imagine short of breaking a gear (as you mention), simply grinding those incredibly hard gears rarely ruins a transmission. I’ve seen a manual transmission that was buried underground. The entire housing had turned to crumbly oxide. The gears just had a light coat of rust and looked like they could be cleaned up and put back in use. Maybe they were protected by the tranny fluid though.
I had a 1988 BMW that I once missed the shift from 5th to 3rd and instead shifted from 5th to 1st while I was going about 60mph.
The clutch shattered.
The mechanic did not find any other damage, just had to replace the clutch.