They don't ban you on all battleye games, for example If you get hwid banned or Battleye Global Banned on DayZ You only get hwid banned from DayZ, games doesn't share banlist or something like that.
Well if the cheat you are using is detected It's possible to get almost instantly banned although on battleye and eac protected games they usually delay those bans up to months to ban as many as people they can ban. ( In our case Our Cheats are Battleye Undetected Since Late 2019 as you can see on https://proofcore.io/status/ page ) That doesn't mean you can't get server banned or manual banned with em Specially on games like PUBG They got tons of server-side anti-cheats and report based manual ban system, I'm assuming you want to buy the DayZ cheat so in that case Only thing you need to worry about is server admins.
Yes As i said before they usually ban people in waves to catch as many as people they can.
Battleye Can Ban your Steam64 id, HWID( only diskdrives so if you switch them you can bypass hwid ban ) and IP
Servers ( Server Admins ) Can ban your Steam64 id, IP Adress and they can flag your game profiles.
RAID0 is currently the best way to Bypass / Avoid Battleye Hwid bans highly suggested
Spoofers Can also get detected Just like Cheats, If you buy public spoofer chances of you getting banned cuz of spoofer is most likely higher than using cheats so I'll suggest you to do RAID0 Instead.