First, thanks to @The Crucible community member to notice something off with laser weapons.

This error was there before re-awakening patch,  Both 1.5.48 and 1.4.21 accessible through betas and didn't suffer from it, but 1.57 also had it.

Both lasers and beams have a "PreparationDuration" value of 7 in the base xml class for the weapon.

As the thing works, there's an immutable firing rate, that is "PreparationDuration" + "ShootingDuration".

Cooldown extends the fire rate with: "Cooldown" - ("PreparationDuration" + "ShootingDuration"), if the value is less than 0, becomes 0, so there's no additional recovery phase.

Lastly effects that affect cooldown don't affect "PreparationDuration" + "ShootingDuration". So if cooldown is lower than the sum of the other properties, cooldown effects may not have real impact in fire rates.

I confirmed this both in the main DLL weapon cycle, and tinkering with values and watching battles ingame.

With current values, lasers have an effective 8 seconds immutable cooldown, and beams 8.2 seconds, here are the current values for reference. In 1.4.21 was a Preparation Duration value of 0.5 seconds for lasers and 3.5 seconds for beams.

In "\Public\Simulation\Battles\SimulationDescriptors[ModuleWeapon].xml":

  <SimulationDescriptor Name="ClassModuleWeaponLaser"  Type="ClassModuleWeapon">

    <Modifier TargetProperty="WeaponTypeEnergy"                Operation="Addition"  Value="1"          Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="Cooldown"                        Operation="Addition" Value="1.8"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDuration"             Operation="Addition" Value="7"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDurationFactorMin"    Operation="Multiplication" Value="0.9"  Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDurationFactorMax"    Operation="Multiplication" Value="1.1"  Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="ShootingDuration"                Operation="Addition" Value="1"          Path="ClassModuleWeapon" TooltipHidden="true"/>

...

  <SimulationDescriptor Name="ClassModuleWeaponBeam"  Type="ClassModuleWeapon">

    <Modifier TargetProperty="WeaponTypeEnergy"             Operation="Addition"        Value="1"          Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="Cooldown"                     Operation="Addition"        Value="6.8"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDuration"          Operation="Addition"        Value="7"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDurationFactorMin" Operation="Multiplication"  Value="0.75"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="PreparationDurationFactorMax" Operation="Multiplication"  Value="1.25"        Path="ClassModuleWeapon" TooltipHidden="true"/>

    <Modifier TargetProperty="ShootingDuration"             Operation="Addition"        Value="1.2"        Path="ClassModuleWeapon" TooltipHidden="true"/>