Does the inclusion of quantitative data in a qualitative research inherently makes the research a mixed-method?

You can refer to my answer in the following RG link that I'd answered to similar question.  Hope it can help.

https://www.researchgate.net/post/Can_someone_help_me_decide_whether_my_study_is_Qualitative_or_Mixed_Methods_MMR

I think that it depends on how you use that quantitative data. In particular, if you use it to generate a set of results that are relevant to your research question, then you are probably doing some form of mixed methods.

Can you tell us more about how you are using the two types of data?

Yes once you use two different methods for gathering data it is called mixed method research. You might use quantitative or charting to clarify questions asked in a qualitative study.

Adding qualitative research to a main quantitative study does not make the research a mixed-method. A mixed method  is purposely design from conceptual stage to address research question (s) that either quantitative or qualitative design cannot alone address. Therefore there is need to combine the methods. It is different from a study that needs additional information or supportive data for completeness sake. It has its unique variants, analysis and report format. Researchers have categorized mixed method as a form of research design just like RCT.  Its central premise is that the use of quantitative and qualitative approaches in combination provides a better understanding of research problems than either approach alone.”

(Cresswell & Clark, 2007, p.5)For instance in mixed-method, there are different variants like Exploratory, Explanatory, Triangulation and Embedded. Your research objective has to fall into any of these forms to make it mixed-method. You also need to show appropriate legend like QUANT, QUAL, quant, qual etc to show the what drives the mixd-methods

I hope this helps a bit.

It depends on the nature of the research. Sometimes, quantitative data is used in qualitative research for triangulation purposes.

Gedion, including numerical data doesn't by itself make the research "mixed methods"; many qualitative studies do this, although not necessarily for triangulation. See attached paper.

As others have said, mixed methods in rooted in a unique paradigm that makes it distinctive and greater than the sum of quantitative and qualitative summative paradigmatic parts. It has its own body of literature. Some good references are given above.

There's a widespread view that qualitative, quantitative, and mixed methods research are each based on (or are) distinctive "paradigms." I think this is questionable. See attached paper.