Pay medical tab with cash even when you're insured?

Which should I do for the example here? A colonoscopy with a cash price of $1625 or pay $5000 (the insurance negotiated rate) ?

The gamble is whether or not I'll reach my deductible for my high deductible plan.

If I use my HSA card, can I then inform my insurer about the $1625 expense and will it count towards my deductible?

There seems to be no easy answer.

https://www.washingtonpost.com/opinions/2023/04/11/hospital-prices-health-insurance-high-costs/