The money supply of bitcoins is inflationary because bitcoins are still being made.

The purchasing power of bitcoins is deflationary because its buying power has historically increased (making other goods decrease in their bitcoin price over time.)

Since the deflationary element has predominated in the years since its creation however, it is more sensible to call it "deflationary" in the whole.

If you don't trust me (or my Finance degree), then google and read the paper of the Bitcoin creator, where he/she/they outlined the economics benefits of Bitcoin. Sorry, can't link to the paper myself.

That's what inflating in value means. Not all inflation is of the general level of prices of goods; you can have asset price inflation, or cost inflation, or in this case, Bitcoin value inflation.

because the supply has a hard upper bound

It's appreciating because demand is increasing faster than supply. The future limit may be driving that demand, but it's certainly not the whole reason, since not all currencies with such an upper bound are this successful.

You're using "inflation" to mean exactly the opposite of what economists usually use the term "inflation" to mean. Bitcoin is experiencing deflation because the value of each bitcoin is increasing.

When people - including economists - just say inflation, that's just an abbreviation for "inflation [of the general level of prices]", out if they're Austrian, "inflation [of the money supply]".

But even if this type of inflation is more commonly discussed, that doesn't mean it's the only, and economists also talk about types (e.g. asset value inflation).

Now, notice I didn't write that Bitcoin is an "inflationary currency", but that it's inflating in value. That's because the former term refers to the first kind of inflation I wrote above, when I'm talking about another.

Why did I use an unconventional type of inflation? Is because while it's technically true that the general level of prices in Bitcoins is deflating, I don't think that's very relevant when almost no product sets its prices in that currency, nor will any economy thus experience any deflation due to it.

At least for now, Bitcoin is more like an asset than a currency, therefore it makes sense to speak of its value inflating, just like we do for other assets.

What I think you really meant to say was: "increasing in both value and supply". And that would be right.

So when Anna Schwartz wrote her paper "Asset Price Inflation and Monetary Policy" where she talks about the "assets whose prices have escalated", she actually means the value of the assets went down? I think you've just invented new economic theory.

An asset price inflation is an escalation of their prices, much like a Bitcoin value inflation is an escalation of its value.

What I think you really meant to say was: "increasing

Why do you think the word "inflation" was chosen in the first place? What does it mean to inflating something?