Cascade effect.
If you have sleep apnea you are not breathing properly when you are asleep.
If you are not breathing when you are asleep you are short of oxygen.
So your blood pressure rises to pump what oxygen you have to where it needs to be.
You wake up because you were not breathing.
Because you are waking up a couple times a minute you rarely go into REM sleep.
You feel tired and fuzzy because you are in sleep debt.
Because you are low in energy you eat more (your body is seeking energy from anywhere at this point).
Because you are eating more and moving less (you after all are very tired) you gain weight.
This also causes your blood pressure to go up.
And it just keeps going. After the cycle has been going a few years if will keep going. What is in motion tends to stay in motion even if the underlying causes is fixed.
Proper sleep is not just nice, it is vital to life.
“So your blood pressure rises to pump what oxygen you have to where it needs to be.”
To pick on just one thing within your hypothetical chain of causation — I have never heard of that. Pulmonary hypertension can occur with chronic hypoxema but chaotic bp, heart rate and respiration would be more likely.