Accuracy of a multimeter over 10 years period

Generally that figure is defined because you are supposed to calibrate your equipment annually.

If you don't.. all bets are off.

You can not extrapolate from one to the other, plus aging will not be linear.

Do I have to multiply "1 year accuracy" by 10?

Well if you could use it without a calibration being needed it's not strictly the case of multiplying by ten because it's like compound interest that a bank might charge.

So if it drifts +1% per year, over ten years you get \$(1.01)^{10} - 1\$ = 10.46%.

Doesn't sound too bad and for tighter tolerances you can certainly approximate to multiplying by ten.

But you do need regular calibrations for this type of equipment, else what is the point of using it?

The simple legal answer is they owe you this accuracy for a year. It the meter fails this within a year you have a warranty claim. After a year (absent another specification) you are on your own. The extreme engineering approach would be for the manufacturer to require drift specs from every vendor and do an error analysis that supports the claim. You can guess as well as I whether they have done that. After a year they have not made a promise. Maybe there is a drift proportional to time^2 or a higher power so things go to pot shortly after one year. In an extreme theory even frequent calibration will not solve this problem.

Practically, shorting the leads together will detect offset errors. It won't help with gain errors. We might measure 1.456 volts on one point and 1.358 on another. Sometimes what we care about is that the first is higher than the second. In practice any time I got that from a meter I would count on the ordering of them, but I wouldn't count on the difference being 0.098 volts. Usually the first is the important fact, not the second. Relative values are much easier than absolute. If you need absolute, you need to be calibrating often and doing careful error analysis. Otherwise you need to develop the skills to understand what you know and what you don't. In practice a 10 year old meter is very useful, but you can't justify it from the specs.