The researcher is best referred to as a observer as participant.
One of the four basic types of observational research is the observer as participant.
As a researcher conducting observational research as a participant observer, it allows the researcher to conduct observations by collecting data with little interaction with the participants.
The researcher is identified by the study participants as a researcher and is also able to join in group activities, but tries to play a neutral role as much as possible while carrying out the study.
As a result, based on the example provided in the question, the researcher is better described as an observer rather than a participant.
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