Check out example codes for "SQLSTATE[HY000] [1040] Too many connections". It will help you in understanding the concepts better.

Code Example 1

On a shared hosting, "unlimited" means other users are unrestricted with their
resource using. Means they can eat up whole pool, while your consumption
remains modest

This is a limit of database's configuration. If you have permission to edit 
the configuration file of your database service, you can change max_connections
value.

You can try running this SQL query (take care about this value!)
	SET GLOBAL max_connections = 512;

and this to get current value of all variables:
	SHOW VARIABLES;
or (for specific variable):

SHOW GLOBAL VARIABLES LIKE '%max_connections%'

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