why would PostgreSQL connection establishment be CPU-bound - postgresql

Question

I have a C# backend running on AWS Lambda. It connects to a PostgreSQL DB in the same region.
I observed extremely slow cold-startup execution time after adding the DB connection code. After allocating more memory to my Lambda function, the execution time has significantly reduced.
The execution time as measured by Lambda console:
128 MB (~15.5 sec)
256 MB (~9 sec)
384 MB (~6 sec)
512 MB (~4.5 sec)
640 MB (~3.5 sec)
768 MB (~3 sec)
In contrast, after commenting out the DB connection code:
128 MB (~5 sec)
256 MB (~2.5 sec)
So opening a DB connection has contributed a lot to the execution time.
According to AWS documentation:
In the AWS Lambda resource model, you choose the amount of memory you
want for your function, and are allocated proportional CPU power and
other resources.
Since the peak memory usage has consistently stayed at ~45 MB, this phenomenon seems to suggest that database connection establishment is a computationally intensive activity. If so, why?
Code in question (I'm using Npgsql):
var conn = new NpgsqlConnection(Db.connStr);
conn.Open();
using(conn)
{ // print something }
Update 1
I set up a MariaDB instance with the same configuration and did some testing.
Using MySql.Data for synchronous operation:
128 MB (~12.5 sec)
256 MB (~6.5 sec)
Using MySqlConnector for asynchronous operation:
128 MB (~11 sec)
256 MB (~5 sec)
Interestingly, the execution time on my laptop has increased from ~4 sec (for Npgsql) to 12~15 sec (for MySql.Data and MySqlConnector).
At this point, I'll just allocate more memory to the Lambda function to solve this issue. But if anyone knows why the connection establishment took so long, I'd appreciate an answer. I might post some profiling results later.