How is the "Adjust memory quotas for a process" user right assignment used in SQL Server 2019?
Can anyone confirm why this is required and what it's function is within the SQL Engine

This privilege when granted to user account will give ability to the account to adjust maximum memory that other process can use. See the official document

This privilege determines who can change the maximum memory that can be consumed by a process. This privilege is useful for system tuning on a group or user basis.
This user right is defined in the Default Domain Controller Group Policy Object (GPO) and in the local security policy of workstations and servers.

The SQL Server, SQL Server agent. SSAS service account should have this privilege to adjust the quota if DB engine deems necessary. But also note that if this is given to user account which is used to run certain queries it can also lead to Denial of Service attack( DoS) by changing the quota.