Why would any entity buy bonds that when matured will not have kept up remotely with inflation? Obviously I'm missing some key idea here, I just have no idea what it is.
Even in societies with financial systems, getting low risk, hassle free, liquid, positive real returns has been difficult for most of history. This just reflects the natural laws of thermodynamics that tell us that everything tends to decay without a constant supply of work and energy. In general, most things require maintenance to keep their worth.
The 20th century was probably the most notable exception. Because of unprecedented demographic and technological growth, positive risk free real returns were easy to find. The recency effect probably explains some of the confusion people have about this. It is possible that under favorable conditions, wealth can have positive returns and even compound into very good long run returns but it is not a guarantee and there is nothing natural about it. It may not continue forever, particularly amidst an aging and retiring population in a world no longer as rich in easy to exploit natural resources.
Maybe they think inflation will stay low. My sense is that at the moment there's a lot of money sloshing around chasing not-so-great returns, so returns on everything are low - capital is subject to supply and demand like anything else.
And much better than anything < 0%.
If you hold it physically, you have to store it and secure it, which costs money.
If you deposit it in a commercial bank, it'll be less safe than German bonds.
When you talk about "money being electronic" you're basically talking about bonds. When people (or companies, foreign governments, etc.) want to hold large quantities of USD they don't really hold USD, they hold short-term US government bonds.
The only truly "real USD" is physical cash, or an account balance at the Federal Reserve (which is available only to banks).
So people don't own bonds just because of the coupon, it's also really the only convenient way to own (something mostly equivalent to) currency -- other than keeping it in a private bank, which is much more likely to fail than the government.
They could keep it in the Fed, but the Fed charges money for the privilege (and I assume so does the ECB and other equivalents)
A record where, though?
Bank "clearing" means that ultimately a bank is keeping its money either with other banks or with the central bank. They're records, but not necessarily interest-bearing, and keeping it with other banks is not risk-free.
https://www.ecb.europa.eu/explainers/tell-me/html/what-is-th...
(I realize we're talking about German banks, and FDIC is a US institution)
If you try to leave your money with the Swiss Central Bank they will charge you 0.75%. Buying bonds is definitely preferable to that. https://www.snb.ch/en/ifor/finmkt/operat/id/finmkt_nz
But there is a pretty wide spectrum between that and what we have now. Gold is a hedge against something like what happened to Yugoslavia, even if it's not a good hedge against the apocalypse.
Having a "prepper bunker" full of expensive supplies is not an asset, it just makes you a target. Having a small cache of things you can easily hide, secure, and trade is significantly better. If you have to bail in your city because things get too ugly you don't need a trailer truck to move.
Any normal person who needs more than a bug-out bag and a passport to survive is doing it wrong.
That said, I agree that gold is probably not that useful in a collapse.
…looks like the market expects 1.57% inflation over the next 10 years, so these bonds are expected to beat inflation handily.
The answer to your question "why would any entity buy bonds..." is: to sell them moments later at a profit.