If you need a quicker way to download RDS DB logs, you can do so through AWS CLI (command line interface).
Although the AWS console also allows downloading these logs, there are disadvantages to this. Since the console is a graphical user interface, you must click/select the RDS instance first, click on the Monitoring tab of the instance, scroll down to the list of instance logs, and even sort the list of logs in descending order to get to the most recent one -- if you are in the middle of an incident and need to look at the logs to diagnose the issue. Then you click on the selected log, click the download button, which will bring up a page where you can right-click the selected log using "save as". In short, too many mouse clicks before you can get to the needed logs.
Another disadvantage is that you are only allowed to download the log files as they are. So if the log file is large, you cross your fingers that the network connection will hold steady and won't disconnect in the middle of the download. If that happens, you have to resume the download and start again.
For faster and more reliable download of RDS DB log files, you can use AWS CLIs instead. Here is how it is done in Linux. The same CLIs are also available for Windows.
First, you run the describe-db-log-files command and combine it with the grep Linux OS command to list the existing log files. You must supply the value for the db-instance-identifier parameter, in this example it is dba-works-01.
dbaworks@dbasrv1:~$ aws rds describe-db-log-files --db-instance-identifier dba-works-01 | grep "LogFileName"
This will return the list of RDS log files for the dba-works-01 instance.
"LogFileName": "error/postgresql.log.2021-05-16-12",
"LogFileName": "error/postgresql.log.2021-05-17-00",
"LogFileName": "error/postgresql.log.2021-05-17-12",
"LogFileName": "error/postgresql.log.2021-05-18-00",
"LogFileName": "error/postgresql.log.2021-05-18-12",
"LogFileName": "error/postgresql.log.2021-05-19-00",
"LogFileName": "error/postgresql.log.2021-05-19-12",
aws rds download-db-log-file-portion --db-instance-identifier help