Does this have practical implications, as in, is this an algorithm that you'd run in practice, or is it mainly a theoretical bound due to constants hidden in the landau symbol?
So most likely, no. This is primarily of theoretical importance (it is now the fastest, deterministic algorithm with a proven bound), but is not immediately a performance gain on existing algorithms.
[1] https://en.wikipedia.org/wiki/General_number_field_sieve
[2] https://en.wikipedia.org/wiki/Lenstra_elliptic-curve_factori...