An older galaxy watch is the only straightforward way to sync with samsung health if you don't want to break the bank. still over 100.
Easiest way would not be to use samsung health...would be google fit...as damn near everything integrates into google fit..good or bad.
The amazfit watches are well under 100, and given your use case it seems like the best fit.
https://www.amazon.com/s?k=amazfit&crid=2NPHVQOVKULO&sprefix=amazfit%2Caps%2C251&ref=nb_sb_noss_1