I suggest parasocial interaction even though the OP ruled it out, because the original meaning has changed over time. Here are some references starting with:
The Wikipedia entry for Parasocial interaction
Parasocial interaction (PSI) refers to a kind of psychological relationship experienced by an audience in their mediated encounters with performers in the mass media, particularly on television and online platforms. Viewers or listeners come to consider media personalities as friends, despite having no or limited interactions with them. PSI is described as an illusory experience, such that media audiences interact with personas (e.g., talk show hosts, celebrities, fictional characters, social media influencers) as if they are engaged in a reciprocal relationship with them. The term was coined by Donald Horton and Richard Wohl in 1956.
The article describes the evolution of the term and its relevance in social media more generally.
The OP rules out a one-sided relationship, but media figures, soap dramas and AI do not have a relationship with the viewer, of course.
Cambridge Dictionary has
parasocial
adjective
involving or relating to a connection that someone feels between themselves and a famous person they do not know, a character in a book, film, TV series, etc., or an artificial intelligence
‘Parasocial’ is Cambridge Dictionary’s Word of the Year 2025
Interest in one-sided parasocial relationships that people form with celebrities, influencers and AI chatbots has driven Cambridge Dictionary's Word of the Year for 2025.
Effects of attractions and social attributes on peoples’ usage intention and media dependence towards chatbot: The mediating role of parasocial interaction and emotional support
It is important to explore the relationship between humans and chatbots to improve human–robot interaction in the era of artificial intelligence. This study aims to explore the effects of attractions and social attributes of chatbots on users’ media dependency and usage intention of chatbots, as well as the role of users’ para-social interaction and emotional support gained from chatbots.
When Human-AI Interactions Become Parasocial: Agency and
Anthropomorphism in Affective Design
Trust is essentially the glue between each of the previous concepts, as it orients people to their social setting, thereby affecting
how they configure the social presence of chatbots, how and what
they communicate, and whether they begin to attribute some socially stable role to a chatbot conversation partner (as in a parasocial
relationship), in addition to informing their perceptions of platform
affordances.
These references support the idea that chatbots and AIs are now included within the scope of parasocial interaction.