There is an evolutionary function to having feelings about feelings, and the function is that if your feelings are not helping you, you tend to feel bad about them, and then you might do something to change them. It is quite possible and people do it frequently.

That just seems related to the evolution of politics. That is, you have to signal feeling bad for asking others to grant you more power (or otherwise do what you want).

Seems like it's mostly signalling. Most feelings about feelings seem to be triggered by a feeling that goes against social norms*. Once the feeling is detected you have a choice of listening to your feeling about that (and pushing yourself in line with your in-group), or coming up with overriding reasons (in which case you will still avoid showcasing your feelings, thus hiding being out of line with your in-group).

I don't think talking about our feelings with others serves much of a signalling purpose (although it could be a signal of group membership, insofar as you accept group values sufficiently to use them to judge your basic feelings), so much as not talking about them does. By feeling bad about a feeling you know not to mention it and lose group membership points.

Although maybe you've already come to a similar conclusion some time in the last 3.3 years.

*at least I can't think off-hand of any cases in which you would feel bad about a feeling which is fully endorsed by your in-group.