The biggest impact is just the number of people who were involved. On the order of 500,000 people passed through the employment records of the Manhattan Project at one point or another during its run (600,000 if you count its yearlong postwar existence). That's approximately 1% of the US civilian labor force, which is pretty impressive for a single project. The vast majority of those people were involved in construction and operation of remote facilities in Washington State and Tennessee, so they would have been relocated for their labor potential to these isolated sites.

Other than that — the project took up a disproportionate amount of resources even with all of those people. Approximately half of the Army construction and raw materials (e.g. steel) went towards the Manhattan Project in its "boom" year of 1943. That's a huge "resource sink" that would have rippled throughout other supply chains, to the degree that it caught the attention of wartime auditors who feared it was a boondoggle since they had not been informed about it.

People living near these sites were aware that huge resources were being spent on them, and contacted their Congressmen, who made lots of trouble for the secretive project staff. There were all sorts of rumors as to what they were doing there — my favorite one about Oak Ridge is that it was rumored to be a pilot colony for Eleanor Roosevelt's new socialist America.

There are certainly more "small" ways in which individuals were impacted by the project, depending on the industry or location you were in. Famously some science fiction writers were told not to write about atomic energy, and several newspapers ran afoul of censorship rules. People living near production or research sites sometimes saw their land bought up from under them by eminent domain (and sometimes challenged it in the courts, which again created secrecy issues for the government). Inventors who worked on topics considered "too close" to project interests (e.g. particle accelerators, neutron generators, and so on) found them put under secrecy for the duration of the war, with no recourse or payment. And so on.

In general in any given domain of activity the Manhattan Project accounted for on the order of 1% of the country's work, input, and output. (So approximately 1% of the patent applications generated during the war were under the auspices of the project, as an example — almost all in secret.) It was the creation of an entirely new industry from scratch. 1% isn't the largest number, to be sure, but it's an impressive one for a project that was essentially secret. So from the point of view of "impact," I'd keep that in mind — 1% is a tangible impact (if 1% of people suffered from some rare disease, you'd probably know at least one person who had it), though it is not an overwhelming impact (unless you're the one with the rare disease).