The weapons do fire independently but as you observed will usually hit infantry, so 4 SHAV is overkill as you will largely be shooting at infantry and if only tanks remain 1 SHAV will still kill a tank per attack.
In practice any SHAV is pretty much overkill as running into something heavier than Medium vehicles is currently almost impossible, I still make super heavy tanks with a SHAV as an RP decision but I do make sure I have a lot of Autocannon and HCAP weapons as they kill infantry. My superheavy tanks carry a SHAV and HAC's which also kill a lot of medium tanks , for pure efficiency HCAPS are better but I overdo it for RP reasons

If you really want to mop up infantry, equip your SHV with as many HCAP as you can fit on it. I usually call this an "IFV". Infantry shots will almost certainly bounce right off your SHVA. Their anti-vehicle units will have to shoot your SHVs to really have any chance at destroying them, but they too will have a lower chance of destroying your IFVs (assuming you have equal armor and weapons tech to each other) because SHVA is literally "super heavy". It's very hard to break.

I also make a "tank" that includes 1 HCAP and the rest are SHACs. So, these too will mow through infantry while also possessing firepower to deal with heavy armored.

And finally, I make a "tank destroyer" which includes SHACs and 1 SHAV, just in case I need that extra firepower to take out something heavier than I can field due to tech differential or after their infantry have been wrecked by my IFVs and I want to mop up the remaining heavies.

Losing one of these hurts a bit since they take a lot of BP to make. You can either deal with it by having a lot of extra production for ground units, or you can do what other players do and be a bit monstrous by having infantry soak up shots. I prefer to have the extra production.

Don't forget HB artillery in the rear echelon supporting your assault forces.

4xSHAV is total overkill. Instead, have them carry a mix of CAP, HCAP and LAC and maybe one HAV. It is extremely rare that AI has units with such armour that SHAV is needed. Mopping up the infantry is always needed and always useful.

Noob here, don't kick, please.

Finally, I've researched biggest and baddest Ultra-Heavy Vehicle (siege Cyclop-class mech) for my ground forces.. but discovered a quite troubling matter.
It is the heaviest unit in my roster - 536size with 4xSHAV! Which means, I have very few shots in my disposal after deploying those beasts in a standard formation.
I predict: enemy numbered infantry will soak up all the shots rendering siege machines mostly ineffective (assuming their low number in formation due to size).

Question for players: how to ensure that shots will hit enemy heavily armoured targets? Not be wasted on infantry?

Thank you!

The fire control to which you have assigned the target has too high a resolution to lock-on to the hostile ships at that range.

A fire control with a resolution of 160 is designed to engage ships of 8000 tons or more. With smaller ships than 8000 tons the range is modified by (Ship Size / 8000 tons)^2. So in this case, to target something of 750 tons, the range would to be less than (750/8000) x (750/8000) x 122.5m, which is 1.08m.

Fortunately, you already have a fire control on the ship than can target small ships or missiles, so you can just move the anti-ship launchers over to the AMM fire control.