How to treat roach nymphs/baby roaches coming up shower drain?

Hi everyone, hope everyone is staying safe and cool during this very hot June. I live in one of those older garage apartments in Montrose and have been seeing increased roach activity in my shower in June, especially with daily 90+ degree weather.

I don't have a tub, just a standing shower. The pipes are metal, old and prone to backups. I used to see a a couple of dead baby American roaches on my bathroom floor in the summer, but now I am seeing live baby roaches that come up from the drain. They fit through the small holes on the metal drain cover I have (please see picture here). I don't see full grown American roaches, and my apartment does not have the small German roaches.

In previous summers, I would pour a bit of bleach down the drain and would not see any live bugs in the shower. Is that the best course of action for these old Montrose apartment pipes? The plumber of the apartment says that is OK to do, and I just want to confirm.

Also, does anyone have any other recommendations I could follow to attack these baby roaches in the shower? I have Bengal spray (not sure how that could help in a drain), Boric acid (may not be effective when water comes), Combat roach gel and roach motel traps.

Thanks so much for your advice. I am trying to keep a sane head in quarantine and reduce my anxiety. I was feeling alone and scared on how to deal with this, so I appreciate the wisdom from my fellow Houstonians. Thanks again and God bless.