Does RAID rebuild time depend on how full the volume is?

This genuinely differs by the storage system, so the honest answer splits in two. State it by what your NAS actually runs.

Traditional RAID: full disk, every time

Classic block-level RAID (including Synology SHR/RAID and standard hardware/software RAID (mdadm)) rebuilds the entire capacity of the drive, block for block, whether the volume is 10% or 90% full. The rebuild works at the disk level and has no concept of which blocks hold data, so how full the volume is makes no difference to the time. Capacity and drive speed set the duration.

File-system-integrated rebuilds: only used data

Systems where RAID and the file system are integrated, ZFS resilver on QNAP's QuTS hero or TrueNAS, rebuild only the blocks that actually hold data. On these, a nearly empty pool resilvers quickly and a full pool takes longer, roughly in proportion to used space. This is a real advantage of ZFS-based systems for large, lightly-used pools.

What this means for you

On a Synology using SHR, do not expect a half-empty volume to rebuild faster: plan for the full-disk time. On a ZFS system, an emptier pool is a faster resilver. Either way, capacity and using CMR drives dominate; state only what your vendor documents for edge cases. The table lists in-stock CMR drives.