What do you call it when a group of people is feeling self-satisfied and praising themselves, even though others don't think them praise-worthy?
Mutual admiration society is apparently an expression in English, used at least as early as 1824.
A group of two or more people, in a workplace or other social environment, who routinely express considerable esteem and support for one another, sometimes to the point of exaggeration or pretense.
I was about to comment about the Swedish expression "klubben för inbördes beundran" that translates to pretty much the same thing, and found the English version while researching it.
The potentially offensive phrase "circle jerk" literally means group masturbation, but is used metaphorically to describe this situation.
Such people are said to be in an echo chamber, in the figurative sense. Or such a group can be called an echo chamber.
Echo chamber -- Wikipedia
An echo chamber is a metaphorical description of a situation in which information, ideas, or beliefs are amplified or reinforced by communication and repetition inside a defined system. Inside a figurative echo chamber, official sources often go unquestioned and different or competing views are censored, disallowed, or otherwise underrepresented.
Here, it could be a group, or just one person praising themselves...
blow (one's) own horn
To boast or brag about one's own abilities, skills, success, achievements, etc.
The Free Dictionary
You could always say that they were / are
Definition of 'gloating':
to observe or think about something with triumphant and often malicious satisfaction, gratification, or delight