This was the reply from the Department of Immigration Latvia.
As mentioned before: If you reside in Croatia as a researcher (you
have a long-stay visa or a temporary residence permit issued by
Croatia for that purpose) you can travel to Latvia and stay here until
180 days without visa in case when research work in Latvia is in the
frame of the same project and you can documentary prove it.
Here is references to the corresponding legal acts:
“A researcher to whom a long-stay visa or a temporary residence permit has been issued in another Member State of the European Union
in relation to research is entitled to reside in the Republic of
Latvia within the validity period of the aforementioned visa or
temporary residence permit for the purpose of conducting the research
work for a period of 180 days in any time period of 360 days.”
(https://likumi.lv/ta/en/en/id/68522-immigration-law, Immigration Law,
(Directive (EU) 2016/801 of the European Parliament and of the Council of 11 May 2016 on the conditions of entry and residence of
third-country nationals for the purposes of research, studies,
training, voluntary service, pupil exchange schemes or educational
projects and au pairing.
That means you do not have to apply for a visa (Schengen C visa) for
travelling to Latvia when purpose of entry is the same research work
as in Croatia.
Researchers don't neet visa to travel to Latvia for 180 days