I found it best to optimize for whatever is a reasonable but useful for users while also preventing any really seriously resource intensive but low value queries (mostly bots / folks trying to mess with your site) to some number that will work with your server main node memory limits.
I navigated to loc.gov and searched directly from the home page.
I was sent to this page: https://www.loc.gov/search/?in=&q=god&new=true&st=
At the top, it says “Results 1-25 of 324,782” and does not mention the limit of 10,000 anywhere.
The number here also seems less misleading because all 324,782 results do seem to exist. It doesn't want to generate a pagination for the entire set, but you could get to them by choosing different formats, date ranges, collections etc. The number Google repors, as far as I can tell, needs to be taken on faith.
But you can subdivide the search results by date and get every item on your original list: https://www.loc.gov/search/?dates=1890/1899&q=god&sp=1808
So, they have and can show you every single one of those 324,782.
You Searched: ALL: God
Your search retrieved more records than can be displayed. Only the first 10,000 will be shown.
Titles List: 1-25 of 10000 https://catalog.loc.gov/vwebv/search?searchArg=God&searchCod...