Please review some of the many hood threads on this forum to gain insight in to the issues posed by kitchen ventilation. @User's comment is reasonable assuming various unstated assumptions, one of which is the assumption that there is a suitable make-up air plan.

There is always make-up air, the question is whether it is adequate. No air leaves the kitchen via the hood that didn't enter the kitchen. If the entry path is restrictive, then (a) there may be a safety hazard with respect to combustion appliances in contact with the kitchen air -- back-drafting carbon monoxide, and (b) the hood flow will be less than one wants.

Whether 400 blower-rated CFM (in practice significantly less actual volumetric flow rate) is sufficient depends on cooking surface temperature and various details about the hood configuration; and one's tolerance for grease and odor.

Ignoring edge effects between a liner and a cabinet, and using the Wolf 22.5 inch by 40.375 inch liner as an example, the effective entry area is assumed to be 6.3 sq. ft. I would recommend 90 ft/min air velocity if wok cooking or hot searing is intended. This requires 6.3 x 90 => 500 - 600 actual CFM. Depending on pressure loss in the hood baffles, the selected blower, and the pressure loss of the MUA system, a 750 - 900 CFM rated (that is, hanging in free air) blower is needed. You will need deliberate, but possibly only passive, MUA for this configuration.

The most optimistic assumption about lower plume velocities from induction cooking would reduce these values to 2/3. That is, a blower rated at 500 - 600 CFM could work. Municipalities enforcing the IBC requirements on MUA will still require some MUA scheme, such as a duct with a powered damper.

A smaller hood is not a good fix for cutting required CFM, because adequate plume capture could be unsuccessful in some cases.

It may be worth adding, as @opaone has pointed out w.r.t. commercial hoods, if the capture or containment volume -- the reservoir -- below the baffles is larger than typical of residential hoods, then plume spillage can be resisted with a somewhat lower volumetric flow rate. I am not aware of any quantification of this effect, due I think to spreading of the plume over the entire baffle space, but in the case of an insert one has this option: namely, to put the insert farther up in the cabinet and extend sheet metal down to the cabinet bottom. I wouldn't want to bet that a 400 CFM rated blower would be adequate in this case, but it would be a possible option to avoid dealing with MUA from a code enforcement POV. Whether combustion appliances are thereby safe is dependent on too many factors to make a pronouncement.

Kaseki any wok cooking or searing would be done outside using other cooking methods(griddle, grill, etc). My understanding is for a 36” cooktop a hood of 36-42” width should be enough? A width of 36” would suffice for induction and I would definitely want to go 42” if doing a gas cooktop instead.

The plume spreading angle for induction is only slightly narrower than for gas cooking.* Hence, hood overlap is desirable in both cases. Without overlap the larger plume generating cooking should be done on a near middle hob.

*Thermal plumes of kitchen appliances: part 2 cooking mode, Risto Kosonen, Hannu Koskela, Pekka Saarinen, Energy and Buildings, Elsevier.

Note that I have no dogs in this fight. You are welcome to experiment with whatever you wish to buy.

What did you go with?