This totally depends on the mortgage / loan contract.
Some are variable rate. For example, where I live, it's common to have Euribor 12mo + margin as the loan rate. This means your interest rate is fixed for the next 12 months at the Euribor 12mo + margin rate at the interest fixing day. The rate stays the same for 12 months, and then is fixed again for the next 12 months.
Some are fixed rate. Typically loans with over 1 year interest rate are classified as fixed. For example, the rate could stay the same for 10 years. If the loan is longer than 10 years, then the market rate changing would affect the loan rate after 10 years from the start of the loan period.
The benefit of variable rate loans is that you generally can pay it back whenever you want.
In contrast, fixed rate loans typically can't be paid back in every single market condition. The reason is simple. If you have a $100,000 10-year bullet loan at 4% rate, you owe $148,024.43 at the end of the loan period. Now, if 10-year market rates lower to 1%, what does it mean for the bank? You would need to pay back $134,004.58 because paying back only $100,000 would not allow the bank to have $148,024.43 at the end of the loan period.
By allowing paying back fixed rate loans in every single market condition would act as a one-way clutch. As a borrower, you could pay back and refinance your loan every time the market rate becomes lower, so you would benefit from reduced rates. In contrast, the bank cannot demand you to refinance your loan every time the market rate becomes higher.
The Euribor rates aren't exactly the same as the central bank rates, but they respond to changes in the central bank rates. The reason central banks adjust their rates is that the adjustments are reflected in the Euribor market rates.
Let the downvotes begin!