Does AC soft start work on any AC

Most ACs are closer to 1000=1300 watts running You say yours is 800

You have 2000 watts peak Your A/C likely peaks (Starting) at around 4,000 watts

How much will a soft start help.. Might get it to 3,000 I don't know

Now.. there is hope.. sort of.. I think Victon made it.

IT's a "Booster" consisting of an inverter/charger and battery in a box.
When the load goes up up up. It parallels with your existing inverter or generator and gives it the boost needed.. Or so said the sales pitch.

I no longer have a link however. And do not know how practical

I'd recommend an inverter upgrade.

Honestly I'm not 100? sure if it was 800w it's already a while ago and I didn't need it since. But it was definitely way below the 2kw. My friend told me that the AC could draw up to 3 times the running current when starting the compressor. But yes the battery was charged and the cable is 35sqmm. And about 40cm long

Ok, how big are the cables? Are the batteries charged? An 800w unit should be easy to start.

I don't think so. But maybe. I have two 200ah lifepo4. They each have a continuous output of 100a. So together they should be capable to deliver 2.4kw

What is your battery setup? It's likely that's the problem, not the inverter.