If the purchase of the watch was made after going Google free and with the intention of using on a deGoogled ROM, the homework should’ve been done first. One may be stuck with an unusable item unless another phone with Google is available.
Watches supported by AsteroidOS or Gadgetbridge would’ve been the ones to look at.
Microg (on LOS) and galaxy watch 4 | XDA Forums
[Discussion?] Galaxy Watch 4 with MicroG and DeGoogle : MicroG
Wishlist: com.google.android.gms.wearable [$135] · Issue #4 · microg/GmsCore · GitHub
There were a number of older threads with related subject. Search for ‘smartwatch’ or the like.
Smartwatch alternative - /e/OS Devices / Request a Device - /e/OS community