I had to introduce a formatter in a few sizeable codebases in the past (few 100k to few million LOC), and I always did it incrementally via a script that reformatted all files that are not touched in any open PR. The initial run reformatted 95% of all files. Then I ran the script every day for ~two weeks and got up to 99.5% of all files and then manually each time one of the remaining ~dozen PRs that were WIP for longer were merged.