By athiest state, I take it you mean one in which:
- the mass population has awoken from the self-righteous, grandiose illusion that their particular and arbitrary relic of history ('holy book'😉, penned and edited by countless unknown authors for various anthropological, cultural and historically political reasons contains the one and only 'truth' about the state of affairs for our existence?
If so, and if the state is not run under the auspices of a dictator in the cases you cited, then we could probably look forward to:
1. Reasoned debate on social issues without deference to the supposed will of imaginary beings
2. Less war - as conflicts will not be spurred by contrasting belief systems which cannot countenance divergent frameworks for proper moral conduct
3. People might get laid more often outside the confines of the sanctity of marriage and actually enjoy themselves
4. People will lose foolish notions of guilt, sin and the like associated with the religious texts
5. People might use their brainpower towards constructive activities instead of prostrating themselves several times a day/week in prayer, church/mosque going, and other associated random rituals
6. Scientific progress will not be hampered by questionable religious barriers
7. People may use their personal skills, abilities and knowledge to overcome difficulties instead of wasting energy on their particular deity to give them strength, courage etc to overcome their particular problem in life
8. Politics at large may become much more sensible without right wing zealots imposing their brand of morality on the masses
9. The subjugation of women encouraged by various sexist texts may be addressed, empowering females to truly take full and equal rights in society at large
10. Lives will not be put at risk by refusal to engage in various medical treatments based on obscure references to arcane literature
11. Persuasive arguments will be based on facts and informed by evidence and research and historical precedents, as opposed to religious absolutes
12. People will generally chill, realize they have been carrying a large weight around on their shoulders for no particular reason, and look forward to understanding life, the universe, and our place in it through a new lens which will actually give us real understanding - instead of being confused by falsehoods peddled by 'flat earthers' who frankly didn't know diddly squat
I could go on, but I think you get the idea...