Looks like the best approach might be to use in-place upgrade tool that ships with Postgres to upgrade to v10 (use Postgres v10 to perform this upgrade). From there you'd be able to create a fresh v14 instance and use logical replication to sync over the v10 database. Before briefly stopping writes while you swap over to the v14 database.

EDIT: Looks like pg_upgrade supports directly upgrading multiple major versions. So maybe just use that if you can afford the downtime.