Remove the set_time_limit(0);
That won't help at the moment.
First, you are accessing both Limesurvey and the SMTP server via unencrypted connections.
That means that these credentials have been exposed to third parties.
Check with your hoster to get a SSL certificate for your Limesurveyinstallation, so that you can access LS via https:
You should check the SendInBlue FAQ for SMTP access:
help.sendinblue.com/hc/en-us/articles/11...issues-with-the-SMTP
If your account is activated and the SMTP settings are correct, try again in LimeSurvey.
Ensure you get the setting for secure SMTP (TLS or SSL). SendInBlue should provide the correct settings. If you still have issues with LS, you can activate SMTP debug and report bug about error messages.
How many emails do you want to send? How many emailadresses are in the list?
Perhaps they are just too many. LimeSurvey is not that good at handling big amounts of emails.