Do I need to pay tax for interest income between £1,000 to £10,000 ?

I have two sources of income. 1) Annual income £48,000 from my payroll job. 2) £1,010 from bank saving interest income. I test myself in https://www.gov.uk/check-if-you-need-tax-return and it said "Based on your answers, you do not need to send areturn for 2023 to 2024." In the test, it specific asked: 6. Did you get more than £10,000 from dividends or savings and investments? So I think I really do not need to submit self-assessment. However I read some where online saying I need to pay tax for interest income >£1,000. So how should I pay the tax without submit self-assessment?

Hi,
"Hi
Your allowances for earning interest before you have to pay tax on it include:
your Personal Allowance
starting rate for savings
Personal Savings Allowance
Please see the guidance at: 
Tax on savings interest
for more information.
Your options if you exceed your allowances are also covered here.
Thank you.

The webpage mentioned: >>If you’re employed or get a pension, HMRC will change your tax code so you pay the tax automatically. To decide your tax code, HMRC will estimate how much interest you’ll get in the current year by looking at how much you got the previous year. Also, >>You need to register for Self Assessment if your income from savings and investments is over £10,000. Since my interest go over my allowance but is under £10,000, I will wait for HMRC change my tax code later. Thanks!