It's internet science with a real kernel, and your instincts about the timing are good. Here's the mechanism: hyaluronic acid is a humectant — it binds water from wherever water is available. In humid air, that includes the environment. In very dry air, the nearest water source is the deeper layers of your own skin, and a humectant left unsealed on the surface can hand that moisture straight to the atmosphere, raising water loss instead of lowering it. This is a known property of humectants generally, and it's exactly why the standard guidance is to pair them with an occlusive or emollient layer that traps what they pull up (https://www.ncbi.nlm.nih.gov/books/NBK545171/).
So the serum didn't turn on you; your climate removed the second half of a two-part system you didn't know you were relying on. The fix is not abandoning HA — its hydration effect is real and fast, measurable from a single application under normal conditions (https://pmc.ncbi.nlm.nih.gov/articles/PMC8322246/) — it's sealing it: apply the HA to skin that's still slightly damp from cleansing, then a proper moisturizer with emollients/occlusives on top within a minute or two. In your climate, a richer cream than you used before the move is probably warranted regardless, and a bedroom humidifier during heating season helps every product you own.
If tightness persists after two weeks of the seal-it approach, simplify: skip the HA, keep the cream, and see whether the serum was ever the problem — sometimes desert air just demands more occlusion, full stop.