It depends on both the laser and the target
Although the laser in the video seems like it is not that great, it is not for a lack of power. That thing has way more than enough power to blow a person's skull open, but as the youtuber explains at 3:52-4:18, the fireball absorbs nearly all of the laser. One of the tricks modern HELs use is laser pulsing. This is where you fire a short pulse, give the plasma a fraction of a second to expand, and then fire another pulse... but there are a lot of factors that play into how long that fraction of a second needs to be.
Heavier elements will expand more slowly; so, a laser overly optimized for flesh might not wait long enough for the plasma ball from a steel strike to expand, but a laser optimized for steel will do less than optimal damage than it could on flesh. You also have to consider spectral banding. Some materials can be vaporised and still allow most of a given wavelength through. Many modern military HELs are designed with this in mind to allow for longer, more destructive pulses. Some lasers also take advantage of multiple wavelength lasers so that the plasma for one constructively interferes with the next instead of blocking it, effectively giving your multiple pulse opportunities per plasma ball. Then there is the width of your beam. Just because you can narrow a laser beam into a pin prick does not always make it ideal. Making a wider area of attack could make a laser strike more debilitating, especially to infantry, but this also reduces the ideal frequency because it will take longer to vaporize the target's surface and longer for the plasma to clear.
In short, the exact ideal pulse rate for any given laser is very hard to say in any back of the envelope way. Engineers spend years determining the answer to this question for each individual weapon system and its intended target(s), and designing a laser that is optimized against such a wide range of materials is especially difficult.
If you really want to optimise this laser, it will need a high speed spectrometer. The first pulse should measure the material composition and rate of dispersion of the target based on its spectral banding and high speed frame counting, and then an onboard computer could use that info to calibrate how long it needs to wait between pulses. So, instead of telling you the ideal pulse rate for this exact weapon and use case, I will tell you that ablative pulsed HELs are typical designed for about 5-100 pulses per second; so, if your laser rifles can adaptively adjust to anywhere in this range, then they should be able to adapt to your wide range of intended targets.
An adaptive laser like this also adds credibility to your setting because it means you can give a plausible answer without having to risk delving into all of the complexities of your exact laser design. When you say, "this thing fires 35 pulses per second using Nd:Glass and a 10 kilojoule power source", anyone who cares enough about lasers to know the difference will likely have all sorts of ideas about why your exact numbers and materials might be off, but if you say it is an adaptive laser that fires between 5-100pps, there is really nothing to argue about. Everyone who knows enough to care will be like, "yup, pulsed HELs usually seem to fall in that range; so, that makes since."
