Muss das nicht als Nebensatz formuliert werden?

Yes, normally.

E.g. the improvements that have still not been made,

the dilemma that still confronts us.

The exact wording would depend on the context.

Is there a grammatical rule to that?

In the two cases with which you began, it is clear to me that a relative clause is needed. But I don't know how one would formulate a general rule.

For comparison, here are some contrary examples that I've found online:

[Photo caption:] Coast Guard members check the still smoldering M/V Mercraft 2 after it was towed to an island. [I did have an example like this in mind.]

When Non-Fungible Tokens (NFT) first came into existence in 2014, they were just another innovation in the still-developing web3 space.

Now with all the uncertainties of what the still barely-proven 2022 F1 designs will do …

On this week's Little Gold Men podcast, a dispatch from the still-ongoing Cannes Film Festival, and a look at the state of the Emmys comedy race.

… launching perfume (including the still-iconic Chanel No. 5), Haute Couture, jewellery lines and, of course, handbags.

Mr. Bankman-Fried is hoping to put a new face on the still-chaotic world of digital assets.

The local revelers ignore the still youngish tech billionaire sipping a pint in their midst.

So one does come across this kind of usage, perhaps especially in journalistic writing.

[Slightly edited.]

@ Hecuba

OT, but I'm curious about the hyphens in your examples...

Do your examples all have hyphens because of your search parameters, or do you think the hyphens are needed?

I think most people wouldn't hyphenate an adverb modifying an adjective in AE, even an adverb that doesn't end in -ly, unless not doing so gives rise to ambiguity or unless the adverb is part of a compound word (e.g. lots of AE writers hyphenate well-known, well-respected & co).

Does BE hyphenate "still" in that context because of a possible ambiguity due to the adjective meaning of "still"? Or is there some other rule in play?

Kurze Anmerkung zum Deutschen:

Sollte wohl immer noch heißen, die Zusammenschreibung ist meines Wissens nicht korrekt.

#11 Re the hyphens, I simply searched for "the still", and copied the sentences as they stood.

The example with "still-ongoing" came from

https://www.vanityfair.com/hollywood/2022/05/...

-- American, I assume.

"Still-chaotic" came from here:

https://www.nytimes.com/2022/05/14/business/s...

The other two -- still-developing and still-iconic -- came from British sources.

I don't see any good reason for the hyphen in any of these cases.

#13 I didn't immediately understand your first sentence, but I take it you mean that the words "still present in M" have to remain together. Yes, I think that may be it. I agree with the rest of what you say.

Thanks.

And yes, that is what I meant, "still present" and "in M." have to remain together. E.g.

"Still present in M, the problem of racism has not yet been tackled in any serious way by the country's politicians."

But I suspect that the meaning of "present" as used in the sentence plays a role, one I'm having trouble to pinning down - because in some contexts, like the one below (found in the Washington Post, also written by a hyphen enthusiast) in which no location is specified, "still present" as a premodifer seems ok, if not particularly elegant.

As the world adapts to the still-present danger it [Covid] poses and people everywhere wear masks on a regular basis, new challenges have surfaced ....