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If you have the space, I recommend 6" wider than the cooktop. Regardless, I would go with 24" deep.
Before we did a partial remodel of the Kitchen in our new-to-us home last year, the 36" induction cooktop had a 36"W x 19"D hood over it. When cooking pasta, I watched as the steam on the center hob escaped the hood and billowed out in the front. When cooking on a side burner, I watched as the steam escaped the sides. Obviously, the hood was not sufficient for even boiling water! I had the fan on the highest setting.
When we remodeled, I put in a 42"W x 24"D hood over the same cooktop - no more escaping steam!

The cost of a large hood has to include the quality of stainless steel used (thickness and alloy -- lots of chromium and nickel involved), the quality of the welds and polish, and to some degree a factor for the manufacturer's reputation. Inserts hide much of the steel and can be made less expensively, but also may have dimensions that are not what you want.
The utility of in-line and remote blowers is that one can insert a silencer (e.g., Fantech LD10) into the duct path between hood and blower and greatly reduce the blade tip turbulence noise emitted from the hood and heard by the cook.
For least complication of getting one's project done, blowers that are compatible with hood controls are recommended. Conversely, one can always put a control somewhere else than in the hood.
Don't forget make-up air (MUA). Scour this forum for relevant discussions.

The cost criterion may be limiting. Frankly, this is not the category deserving economic restraint. Not only is good ventilation needed for minimizing household grease and ill effects from cooking effluent, but these issues justify the significant associated cost (both direct and architectural) of the ventilation system.
The Wolf Design Guide has their line of inserts, and you might as well review them for example designs. I have a Wolf Pro Island hood, not an insert, so I have never examined one. I also have an in-line silencer and roof blower (sold by Wolf, manufactured by Broan/NuTone).
Inserts are also called liners in many cases.
You might check out ModernAire to see what they may have. Note that they build to order if you have some concept in mind that makes sense.
BlueStar absorbed Abbaka, whom I had considered competent in blower design, and I see at their website that they have liners.
It is necessary to understand that after trillions of dollars that had no stored labor input were injected into the economy circa 2022, the inevitable delayed inflation effect is now upon us, and the cost of ventilation components in actual value is probably not yet even at catch-up with, say, 2008 price labor values, which themselves were soon to be driven up by 2008 banking crisis money flooding. Under some personal conditions and guesses abut the future, one might consider buying now and paying off with degraded dollars in the future versus cash now.

Thanks all who commented so far.
The wolf pl402212 is definitely on my radar.
Trade wind VSL400 22" deep coupled with a Fantech FKD10XL inline blower (this is who manfuactures the tradewind inline blower) is also getting a serious look from me as a budget option being around $1500 for both.
Still unclear to me if the vent-a-hood traditional baffle M40PSLD would be compatible with any inline blower, but probably would work fine if I used an external controler for the fan. Not sure.

The VAH M40PSLD insert will not work with a remote blower. It is designed to use their internal blower. It will not have any way to connect the duct pipe. You should be able to find many options for a insert that is designed to work with a remote/inline blower.
Regarding BOOST technologies -- here is a less emotional and more factual breakdown of why I will move from hidden induction, uninstalling my Invisacook, in the near future, though my comment about the Boost on my Invisacook stands,:
it depletes the power access of ALL burners to low -- below medium -- settings and severely hampers my cooking efforts, but would not if I was only making a simple dish for a couple of people -- I find it is more of an irritation when cooking for 4 adults or more, and thus instead of coil ring separation I will move to a zone unit:
Hidden Induction (e.g., Invisacook)
Max Boost Power
Typically 3,000W to 3,600W max shared across a pair of coils.
Sustained Boost Time
Short (often limited to 5–10 minutes or cuts out early due to heat).
Thermal Barrier
High resistance: Must push energy through 12mm to 20mm of solid porcelain/stone countertop.
Coil Density & Coupling
Spaced-out, fixed individual coils. Energy dissipates significantly before hitting the pan.
Full-Zone Induction (e.g., Gaggenau CX 492 / Thermador Freedom)
Max Boost Power:
Typically 3,700W to 5,500W per active pan zone.
Sustained Boost Time:
Long (10 minutes standard, auto-reverts to level 9 without overheating).
Thermal Barrier
Minimal resistance: Separated from the pan bottom by only 4mm of engineered glass-ceramic.
Coil Density & Coupling:
Massive matrix of overlapping micro-coils that dynamic-track the exact shape of your pan footprint.