It doesn't look like MySQL has any concept like a template database. You could still migrate up a pristine database, use mysqldump to produce a schema, then load that into a series of test databases. It of course won't be as quick as the low level copies that Postgres is doing with a template database, but it'd be faster than re-running all your migrations.

OOC — I've been trying to gather real world anecdotes on who is using MySQL these days given that even some of its biggest traditional champions like PlanetScale are talking a lot more about Postgres recently. Are you using MySQL as part of an existing project that was started years ago, or do you still intend to use it for new things going forward?

In theory you can do filesystem-copy-speed population of large seed data using InnoDB's transportable tablespaces feature. For the test db use-case specifically though, unfortunately it's far less ergonomic than Postgres template databases.