If you're doing a migration from Cloud to Server, I would expect you to create an XML backup in Jira Cloud. You can then use that XML backup .zip file when importing your data into Jira Server. If you follow that method, it will migrate all the Jira data in that backup, including the filters themselves. This is actually the method I would recommend here. I will try to better explain why below.
I could understand if you were wanting to try to export the data from Jira Cloud into some format like CSV to keep your issue data, but if you do that, you're going to be missing out on lots of other data like workflows, project settings, and of course filters.
Jira Cloud doesn't give you access to the database directly. If it did, you could run a SQL query such as
select * from searchrequest;
Which would be the full proof way to see all the filters in a Jira site and their JQL details. To try to do this via Jira itself or even via the REST API, you run into problems such as private filters where even admins don't technically have access to see them. In which case, you can't be expected to actually export all the filters in a system because you'd have to impersonate potentially every single user in Jira, know the filter ID, and then perhaps create a script to call the REST endpoint of GET /rest/api/2/filter/{id} to gather the results.
Because this other method is much more complicated, I think it would be preferable to simply migrate the Cloud data into a fresh Jira Server instance per Migrating from Jira Cloud to Server. Even if that instance is just temporary until you can get direct access to that Jira SQL database to run that query, it still seems like a better way to me in order to extract that data.
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