This is the Bucket Head vacuum, a wet/dry vac attachment that works with Home Depot’s 5 gallon buckets.
Sorry, it doesn’t come with a bucket, but sourcing one should be easy enough. It might be compatible with other buckets, but they mention Home Depot’s specifically.
The vac comes with a 1-1/4″ x 4-foot hose and a filter. The power cord is on the short side, at 6 feet long. You can also use it as a blower.
I haven’t used this model, or anything like it before, but I’ve heard good things over the years.
There are pros and cons to a design like this. On one hand, it’ll be compact and easily portable. On the other hand, buckets don’t come with wheels, and so you won’t be able to roll it anywhere.
It has a short power cord, meaning you don’t have a lot of cord to manage, but you also cannot stray far from an outlet without using an extension cord.
The Bucket Head is probably better suited for lighter duty cleanup tasks.
Want something different? Shop-Vac makes something similar, the “Power-Lid,” and from the power draw specs it looks to be a little more powerful.
See Also(Shop Vac vac head via Amazon)