Using an abbreviation of another language in the abstract

You could refer to the German research project by acronym without referring to the full name or you could omit the acronym entirely. The former is perhaps better when the acronym is well known; the latter when it isn't. Since you'll surely be providing the full name, acronym, and translation later, either should be fine.

I suggest that a footnote be avoided, because abstracts get decoupled and such a footnote will be lost.

Given that

STEER: Erhöhung der STEuerungskompetenz zur ERreichung der Ziele eines integrierten Wassermanagements (Increasing Good Governance for Achieving the Objectives of Integrated Water Resources Management)

isn't particularly long, you could just include, assuming your abstract isn't limited by a word count.

As far as I understand, there is no reason why you cannot include the original German with its translation in the abstract, better than in a footnote — which typically don't play well with abstracts.

I would write something like:

In this thesis we refer to X work on the STEER (from its German acronym Erhöhung der STEuerungskompetenz zur ERreichung der Ziele eines integrierten Wassermanagements, Increasing Good Governance for Achieving the Objectives of Integrated Water Resources Management) project.

The only reason not to include it directly in the abstract would be not having enough characters available. In that case, I would do it like:

In this thesis we refer to X work on the STEER (Erhöhung der STEuerungskompetenz zur ERreichung der Ziele eines integrierten Wassermanagements, Increasing Good Governance for Achieving the Objectives of Integrated Water Resources Management) project.

There are no strict rules; you must try to balance clarity, length, and readability according to your own best judgement. As others suggest, spelling it out in full is not dreadfully long:

This thesis builds on the work of the STEER project (Erhöhung der STEuerungskompetenz zur ERreichung der Ziele eines integrierten Wassermanagements, Increasing Good Governance for Achieving the Objectives of Integrated Water Resources Management).

But if you feel this makes the abstract too long (e.g. if you must follow a strict word count/space restriction), or less readable, then there are many other alternatives, e.g.

This thesis builds on the work of the STEER project on governance for water management.

with the full name and translation either given in a footnote, or not mentioned in the abstract at all — the reader who wants to know can flip ahead to the introduction or a later section. In the main text, something like this would be too concise (unless the STEER project is extremely well-known), but in an abstract, conciseness and readability are high priorities; giving thorough details is a much lower priority in an abstract than in the body of a text.