That's the fix, of course, but what about all the embedded software that will last enough to cross that barrier but that won't be upgraded from its 32bits timestamps?

You'd have to find it, too. How many companies have manufactured devices with embedded software that have gone out of business, devices for which no manuals exist anymore, etc?

FWIW, the year 2027 has the same weekdays as 2038. If the worst comes to the worst, setting the clocks back 11 years on unremediated systems has a chance of allowing them to keep working.