How much space do I need to allocate for time machine

Do not partition a Time Machine drive for any other usage. The Time Machine drive should be 2 - 3x the size of your Mac's internal storage capacity, and for macOS Big Sur and later, should be formatted as APFS using Disk Utility.

People think in base 10 and thus want to think 1000 bytes (e.g. 10³), but computers use base 2 numeration and so 1024 is 2¹⁰. We want to use kilo to express units of 1000 but a kilobyte of drive storage is a kibibyte (KiB) whose value is 1024. And it follows, with mebibyte (MiB = 1048576), gibibyte (GiB = 1073741824), and tebibyte (TiB = 1099511627776). You can dispense with the math and follow the TM drive sizing in the first paragraph.

you want the partition to be at least two times the capacity of your local drive. and it is often recommended here to have three or more times the capacity of your local drive.

but rather than partitioning the drive, as affordable as external HDDs have become, why would you not want to get a dedicated drive for TM backups alone?

Your 2 TiB system drive (2 * 2⁴⁰ bytes) would require the following storage on your NAS assuming the 3x TM storage factor:

(3.0 * (2 * 2⁴⁰))/2³⁰ -> 6144 GiB or 6 TiB

Understand that the AppleShare implementation on the NAS side is from open source reverse engineering and cannot possibly match changes that Apple may inevitably apply to macOS that might break your NAS backup solution. A firmware update from your NAS provider could also break this handshake. MacOS Big Sur and Monterey expect the Time Machine filesystem to be APFS and I doubt your NAS provider offers that solution.

I have had a Synology DiskStation in the basement for years and never used its Time Machine service for backup. Always to a locally mounted and sized TM dedicated drive per Mac.