This is true to an extent, men 18-60 aren't allowed to leave unless they have a disability, are have dual citizenship, are seeking permanent residence elsewhere, are on a business trip, studying abroad, or have a large family.
The delays most likely have to do with the newly instated Biometric Passport system and the mandatory proof of financial solvency. Biometric Passports hold your personal information along with your fingerprints, photographs of yourself, biometric facial data, and iris scans. The reasoning behind the passports is simply to reduce identity theft, keep national security healthy, and discourage illegal entry by terrorists. The proof of financial solvency is to make sure those who pass through the boarder are able to support themselves financially after they enter the country. The post you cited is from August and that's when these new measures started being enforced. Repair work has also been taking place, which started in May and is still ongoing today, and which is expected to cause significant delays until the repairs are complete. With the combination of new paperwork systems and requirements, plus the addition of repair work, it makes complete sense that there would be delays. The repair work is expected to wrap up in December of this year, but until then, it's safe to assume that these issues will persist.
Travel Restrictions:
https://tourservice.com.ua/en/blog/visa-free-countries-ukrainians-2025/
Repair work:
https://visitukraine.today/blog/6108/queues-at-the-border-with-poland-in-may-and-june-2025-repairs-at-checkpoints-and-alternative-routes#at-which-border-crossing-points-with-poland-will-there-be-delays-list-and-dates
Changes to immigration policy:
https://visitukraine.today/blog/6785/crossing-the-border-with-poland-in-2025-all-the-new-rules-ukrainians-need-to-know#basic-rules-for-crossing-the-border-with-poland-in-2025
Biometric Passport testing:
https://visitukraine.today/blog/6913/queues-at-the-ukrainian-border-poland-tests-a-new-citizen-control-system#how-does-the-new-system-work
What are Biometric Passports:
https://photoaid.com/blog/biometric-passport/#:~:text=A%20biometric%20passport%20(an%20electronic,benefits%2C%20and%20how%20they%20work.
When repairs will end:
https://visitukraine.today/de/blog/6577/repairs-on-the-border-with-poland-the-ustyluh-zosin-checkpoint-will-operate-with-restrictions-until-the-end-of-december#what-restrictions-are-in-place-at-the-ustyluh-zosin-checkpoint
