rescue beagle three weeks in showing classic separation anxiety symptoms and i cant tell if were still in the adjustment window or if this is something we should be naming and actually treating

Cooper is a 4 year old male beagle we pulled from a rural shelter 3 weeks ago today. backstory we know is thin, he was a stray for an unknown stretch and the shelter had him 8 days before we got him. neutered at intake. body condition was a 3/9 when we picked him up, hes already up to a 4 with regular meals. for context my partner works hybrid (2 days in office, 3 home) and im fully remote, so the longest hes been alone since we got him is roughly 4 hours twice a week.

the behaviors. he follows me room to room, will not settle unless hes on the same furniture as one of us, and if we close a bathroom door between us he scratches at it within about 20 seconds. the alone-time data we have, he barks intermittently for the first 30-40 min, then settles, then starts a low whining pattern around the 2 hour mark that doesnt fully stop until we come home. weve seen the bark via the wyze cam. no destruction so far, no accidents, eats his kongs when we leave them. heart rate (per the wyze, rough proxy) seems normalish.

what im weighing is, is this still adjustment phase territory where we should just keep doing what were doing (predictable routine, calm departures, low key returns, mental enrichment, gradual alone-time increases) and give it another 4-6 weeks before naming a diagnosis, or is the velcro behavior plus the 2hr whining pattern enough that we should be calling our vet to discuss the SA workup now rather than waiting. friends are split, half saying "give him 3 months minimum before you decide anything," half saying "the longer you wait the harder it is to address." anyone walked the same fork with a rescue in the 3-week window, how did you decide.