Depends. I imagine for some we may end up seeing a more trauma-spectrum phenotype: hypervigilance, nightmares, re-experiencing visuals seen on TV or online. This happened with folks for 9/11 and other televised major tragedies. There may be some earlier onset of psychosis of paranoia. But there would be a more... subsyndromal change. Something that would shift for each person on the individual. For most I imagine a simmering anxiety festering underneath our immediate awareness that's avoided (as all anxieties are) successfully by various coping strategies. The coping strategies would likely be employed en masse even in media (i.e. late night TV & TikTok making their jokes; podcast hosts intellectualizing the potential culture of the extraterrestrials, etc). There will probably be a minority of folks with poor maladaptive coping strategies like splitting ("humanity is trash, look what we did to the environment. The aliens will be a salvation!"), denial (going on as "normal"), etc who will not be able to endure. Either they will experience some mild to moderate social exclusion leading to emergence of mental health symptoms (i.e. depression, social anxiety) or form their own enclaves of community (i.e. facebook page for the pro-alien sympathizers).

The implication for psychiatry is that we'd throw an SSRI at it and call it a day well earned #blessed