1250W ÷ 12V = 104.16A uncorrected for inneficiency, 120.44A corrected for 15%.
A battery pack, whether it is 1P4S or 2P4S will still behave the same with regards to load/charge handling which is limited by the BMS to 120A out & 60A in MAX per pack (and that is to limit, not suggested) FET Based BMS' should ALWAYS be derated by 20% for safety & longevity.
4 Equal packs should divide the load/charge by four, so that 120A draw will be 30A per pack in parallel.
Packs in Parallel will stay close to each other but individual pack voltages will float up/down during operation which is normal, as long as it is not excessive. IF all of a sudden one pack goes out of "sync" that is an indicator that something is wrong. It is quite normal to see some fluctuation / variation though, and seeing 1/2V difference is fine, more than that start looking at connections and links.
--** provided **-- the battery packs are identical in capacity & config. If using different AH packs things vary more at Hi/Lo ends of the voltage curve.
You stated that you have 4 packs 2P4S with 800AH. but not cell size.
Normal LFP specs are 1C Discharge & 0.5C Charge C-Rates. so for a 100AH cell based pack, that is 100A Discharge for 1 hour and 50A charge rate for 2 hours.
The general unwritten rule is to not exceed 250A draw from a battery bank (excluding surge handling).
This translates as 12V=3,000W, 24V=6,000W, 48V=12,000W