Data skew is the likely cause for all of these issues, such as record locking, long search times, and long record save times. Data skew is a condition that occurs when a large number of child records are associated with a single parent record, or when a large number of records are owned by a single user. Data skew can affect performance and functionality, such as locking records, slowing down queries, and increasing save times. TDTM, insufficient code coverage, and insufficient data storage are not likely causes for all of these issues. Reference:
https://help.salesforce.com/s/articleView?id=sf.data_skew.htm&type=5
https://developer.salesforce.com/blogs/engineering/2012/04/avoid-account-data-skew-for-peak-performance.html