We have been seeing some issues crop up with thanks to the relative newness MySQL 8 as well.
In the meantime, there are some great tidbits here: Data contains characters which are invalid in the target database … Specifically, the WPMDB_STRIP_INVALID_TEXT constant.
Also, you may have luck converting the collation on the tables that are a newer collation such as utf8mb4_0900_ai_ci to a more compatible one by running:
ALTER TABLE <table-name> CONVERT TO CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_520_ci;
(I recommend backing up the table/database prior to doing this!)