Will too many tables slow Mysql down?
Overall, splitting tables adds overhead for a perceived benefit that isn't there. Tables of a few billion rows do need to be carefully designed as far as index and normalization, however splitting adds computation /software overheads and may generate far worse queries.

To directly answer the question:

Too many tables on disk will have no impact on MySQL (unless you have a filesystem that can't rapidly open a filename from a very full directory (mitigated in 8.0 (frm data in tablespace) and innodb_file_per_table=0).

As far as active tables, those being used frequently in queries there are effects from:

table_open_cache limits the number of tables cached and so does innodb_open_files.

Exceeding these cache limits will cause tables to close and open and need to be re-examined adding overhead to queries.