This week, KataGo finished a project to try to "solve" 7x7. The results are posted on a site here, where you can browse a tree of the optimal or near-optimal lines of play from the opening position and many other variations.
https://katagobooks.org/
Also you can find some commentary on the highlights, including a variety of seeming new discoveries and moves that may have been missed by earlier human attempts to solve 7x7. Nothing mathematically rigorous of course, you're not going to get that with deep neural nets and the limited-depth search of MCTS, and 7x7 is probably still way out of reach of rigorous solvers. So there's always the chance of mistakes and blind spots and new moves yet to be found, but hopefully this book is close to perfect in practice. There are many variations with high uncertainty off the main line particularly after both sides have made mistakes, but all the main lines and the most important refutations should be explored very deeply.
Hope you enjoy it! And on the off chance you find any major errors in the book, let me know. I can get KataGo to spend another billion playouts focused on those lines to fix it.
I think with some more compute, optimal 8x8 is already well within reach right now - it will be more uncertain than 7x7, but in practice I think it is also just about possible to enumerate nearly all the optimal opening lines with high accuracy even if they can't be rigorously proven.
Beyond that, as far as I can tell, 9x9 could almost be within reach before long, with a dedicated effort. But it might take a bit more training to be truly feasible. KataGo is still improving at https://katagotraining.org/, any spare GPU power or contributors can help!