I bought a 9000-watt generator for when we lose electrical power in winter, mainly just to keep heat & lights on.
It'll live on my back porch, under a carport, but still subject to blowing snow.
I'm thinking an enclosure is a good idea, not too tight (see BB in A-body ) with a vented side(s) & hinged or removable lid.
(Home's already wired/boxed).

Am I over-thinking this ?
Any suggestions before I craft another monument ?

It wouldn't hurt and be sure to vent the exhaust fumes out of the carport so they won't collect and smoke you out.

Consider keeping mice out when not running.

Yeah, some kind of tailpipe extension would be a good idea, and yes, the box would also keep the field mice away.
Probably gonna shop those garden enclosures, see if that'll work.
Finding a power cord is proving to be, um, interesting. I only need 10-12 feet, which is apparently ultra-rare.
May be better to have my electrician fab one up.

Make sure you elevate it a few inches to keep it out of water puddles. When inside the structure, keep the exhaust off of wood. I have seen hot exhaust catch siding on fire.. Make sure snow does not build up around it.

The porch is raised, about 6".
Carport is open on 3 sides, plenty of air & breeze.
Definitely will pay attention to heat & exhaust output.

What fuel? I would be hesitant to have a liquid/gas fueled genset on or near any flammable occupied structure or flooring. I have a lot of experience with gensets near people, and the exhaust fumes are seldom predictable, and of course potentially very deadly. An interior carbon monoxide detector would be a nice addition.

What fuel? I would be hesitant to have a liquid/gas fueled genset on or near any flammable occupied structure or flooring.

Thats like being afraid to park your car in a garage.

I keep a 7k unit full inside my back mud room, when needed roll it out on the raised back porch with the ex facing out.

Still here after 15 years doing so.

I swap the gas out yearly and inspect fuel line, ect.

I don't fuel my car in a power outage in my garage in the middle of the night when its running or hot and the family sleeping inside, but be my guest.

Check with the building department in your area for regulations concerning generators installed in/on/near wooden structures. The generator is noisy and that may be amplified near a building. I'd also look into vibration isolator pads to dampen vibration near the unit.

OK
So its a not a whole house unit right?
So how are you hooking up every thing? That you cant find a rubber 10/4 cord ? to run 30 amp as that's all the breaker on the unit will do?
Are you wanting to keep it out side all the time? Or are trying to cut the noise down when running it?

Gasoline power.
Mainly just to keep heat & well pump on, though a few lights will fit into that output.
I'm not that concerned with noise in comparison to that, nor running everything I own.
I'm very careful about gasoline, unit holds enough to run 12 hours or so, would not fill it when hot or running.
Everything here is wood, live in a forest, so fire prevention is a religion.
I plan on adding/using metal near hot surfaces & dealing with exhaust.
I see some plastic garden-style enclosures, reluctant to do that.
Location partially driven by snow from shoveling roof, partially by exposure, partially by keeping cord length down (efficiency).
I handled the cord about an hour ago.

This youtube clip is a segment of a “This Old House” episode where they demonstrate the installation of an interesting kit for using portable generators with house electrical systems

https://www.youtube.com/watch?v=d9V4RjzUXV8

Also check out this device that goes between your electric company meter and house wiring to connect a generator available at Home Depot

https://www.homedepot.com/p/GenerLink-30-Amp-Meter-Mounted-Transfer-Switch-MA23-N/301961623

For sound reduction,
check out “Sonex” waffle surfaced foam,

https://sonex-online.com/

and the pre-fabricated sound reduction fences
made for Outdoor air conditioning units

We left our portable in the shed. When we hooked it up, we placed it on a flat spot and put a deck table umbrella through some zip ties on the handle to keep rain off it from above. Still got wet from the side, but was looking at an enclosure. I have seen some around that look like a mini shed and are used for trash cans. Keeps the critters out, top lifts for access to put trash in and sides fold out to get cans out. Maybe something like that would work? You don't want to keep it totally enclosed when running so some blowing rain will get in no matter what you do. We have since upgraded to a whole house one and love it.

I live in the country in an area that on average losses power 6 times a year. Trees falling on lines, 50 year old transformers blowing, dogs pissing on telephone poles....no power.

I use to back feed into the box with a gas generator like yours. The best thing I did was install a Generac generator 2 years ago. It is plummed into the natural gas line. There are propane versions. 11K Kw powers 70$ of my home. Easy payment/financing thru Generac. No more refueling in 20 degree weather.

I got a 10% Veteran discount at Home Depot and 2 years at 0% with their credit card when we got ours.

You're supposed to use some sort of transfer switch when using a generator to prevent it from back feeding into the lines and killing someone.

For a generator enclosure you're best off to either cover it with an old car cover or something else or make some sort of light crate that you can take off it when you need it. Portable generators aren't meant to be run in an enclose so having it inside one when it's in use could damage it frmo the heat and fumes. It's meant to hold up to the weather anyway so it sohuldn't be a problem being exposed when it's running.