Backflow Floods

Toilets and sink backflow 1-2x/year, under very heavy, fast rain.
Water floods gym from rear bathroom, rains into basement through floor.
Water floods kitchen from front bathroom, goes as far as 1/2 way across space. When viewed from the basement, tends to "rain" in about a 5-15' radius from location of upstairs water fixtures.
Basement floods soak ceiling, accelerating ceiling sag, and other unknown effects re: rot and pests.
Response in the past has been to snake main drain. Results of this snaking (e.g. was a blockage detected, material removed, etc.) are unknown.
Backflow prevention mechanisms exist:
According to neighbors: 583, 585, and 587 (we are 585) all have issues, not clear if this means slow basement wall leaks or backflow issues.
Mitigation thoughts
Short article discussing backflow and backflow prevention devices: https://aquacarewater.com/what-causes-backflow-in-plumbing/
Another, with more detailed listing of devices: https://www.nfpa.org/news-blogs-and-articles/blogs/2022/10/28/backflow-preventer-types
Yet another, basically identical to above, diff pics and text: https://school.sprinklerwarehouse.com/backflow-devices/types-of-backflow-preventers-overview-of-four-common-backflow-preventers/
Yet another, basically identical to above, diff pics and text: https://backflowdirect.com/blog/understanding-the-different-types-of-backflow-preventers
Specific explanation of difference between Pressure Vacuum Breaker (PVB) and Reduced Pressure Zone (RPZ): https://www.bigfrogsupply.com/blogs/big-frog-blog/the-difference-between-a-pressure-vacuum-breaker-and-a-reduced-pressure-backflow-preventer
^^^ backflow prevention valve placement info via plumber via electrician
Plumbing services to check with
Misc info
from: https://www.nyc.gov/site/dep/about/backflow-prevention-frequently-asked-questions.page
Cost
Where to find contractor
Licensed backflow testing people in Queens County
https://www.health.ny.gov/environmental/water/drinking/cross/backflow_testers/queens.htm
This list doesn't have contact details. via general search I found one person listed under "Maspeth":
https://nycmpc.org/members/?id=81926155&terms=%22armon%22
https://skaggswalsh.com/nyc-backflow-prevention-requirements-sw/