Thought this might be interesting data to look at. I used 2019 because it's the latest year with complete enrollment data and complete teams data (there were major fluctuations due to Covid state to state in 2020 in the latter depending on how any given state chose to report their data). I couldn't get any better data than K12 public school enrollment - I had hoped for at least secondary school data - but in general, you can assume that total secondary school enrollment (counting non-public schools) is around 55% to 65% of these numbers, and correspondingly the ratio goes up by around 50% to 80%. If it helps in interpretation, we can estimate that in the US overall, approximately 0.35% to 0.4% of secondary school students participated in Science Olympiad in 2019.
Looking at the state-by-state breakdown, many of the numbers will be as expected to people familiar with the number of teams by state patterns. North Dakota and Delaware are quite predictably at the top of the list, though I wasn't expecting to see Montana so high up. Among the large states, North Carolina and Michigan are substantially above the national average, while Texas and Florida are substantially below it. Do remember that there are many potential reasons why a state might be high or low in this ranking.
K12 pub. enr.,# teams,State,/100k 267976,9,West Virginia,3.4 5433471,240,Texas,4.4 495291,27,Arkansas,5.5 698891,41,Oklahoma,5.9 1141511,70,Arizona,6.1 780882,49,South Carolina,6.3 711783,47,Louisiana,6.6 609507,41,Oregon,6.7 514833,37,Iowa,7.2 492640,38,Nevada,7.7 138975,11,South Dakota,7.9 471298,41,Mississippi,8.7 87074,8,Vermont,9.2 2846444,265,Florida,9.3 1400069,131,New Jersey,9.4 138405,14,D.C.,10.1 677031,72,Utah,10.6 310522,34,Idaho,10.9 889304,99,Minnesota,11.1 962297,111,Massachusetts,11.5 1289367,157,Virginia,12.2 180461,22,Maine,12.2 6272734,841,California,13.4 526634,72,Connecticut,13.7 1123736,157,Washington,14.0 178515,25,New Hampshire,14.0 896827,126,Maryland,14.0 911536,129,Colorado,14.2 739716,112,Alabama,15.1 50694061,7874,USA Overall,15.5 1767202,281,Georgia,15.9 94313,15,Wyoming,15.9 859333,152,Wisconsin,17.7 1695762,306,Ohio,18.0 677821,123,Kentucky,18.1 130963,24,Alaska,18.3 1055706,194,Indiana,18.4 1007624,192,Tennessee,19.1 1730757,334,Pennsylvania,19.3 1982327,383,Illinois,19.3 913441,201,Missouri,22.0 2700833,686,New York,25.4 497733,128,Kansas,25.7 333537,93,New Mexico,27.9 326392,108,Nebraska,33.1 1504194,514,Michigan,34.2 143436,52,Rhode Island,36.3 181278,68,Hawaii,37.5 1552497,636,North Carolina,41.0 148844,117,Montana,78.6 88493,106,Delaware,119.8 113845,141,North Dakota,123.9