Date of Monday in a given week of the year
The week number of a given date @d, when weeks are defined as starting on Mondays and when we agree to number weeks of the year from 1 through 53, is given by WEEK(@d, 2). Here is a way to get the date of Monday in that week:
set @d='2025-1-31';
select makedate( left(yearweek(@d),4),week( @d, 2 ) * 7 ) as 1stdayOfWeek;
+--------------+
| 1stdayOfWeek |
+--------------+
| 2008-01-28 |
+--------------+
set @d='2024-7-15';
select makedate( left(yearweek(@d),4),week( @d, 2 ) * 7 ) as 1stdayOfWeek;
+--------------+
| 1stdayOfWeek |
+--------------+
| 2008-07-14 |
+--------------+