prisma: Timed out fetching a new connection, even with high connection_limit

Bug description

When I kick off many queries concurrently, I get this issue:

Timed out fetching a new connection from the connection pool. More info: http://pris.ly/d/connection-pool (Current connection pool timeout: 1, connection limit: 100)

I expect to NOT get this issue

How to reproduce

async function example() {
  const prisma = getPrisma('some_url?connection_limit=100&pool_timeout=1');

  const range = [...Array(10).keys()];
  await Promise.all(range.map(async (val) => {
    await prisma.nft.findMany({take: 10});
  }));

  console.log("done!");
}

When I run this code, I get this error:

Timed out fetching a new connection from the connection pool. More info: http://pris.ly/d/connection-pool (Current connection pool timeout: 1, connection limit: 100)

However, based on the Prisma docs, it seems like I should not be running into this.

If there are no idle connections available in the connection pool, the query engine opens additional database connections and adds them to the connection pool until the number of database connections reaches the limit defined by connection_limit.

Since my connection_limit (100) is much higher than the number of queries I’m kicking off (10), I don’t get why I’m running into this issue.

Also, my DB supports a maximum of over 3000 connections

One more note: weirdly, if I use connection_limit=1, I get no errors

Expected behavior

I expect all my queries to execute successfully

Prisma information

Not needed

Environment & setup

• OS: Mac OS
• Database: PostgreSQL
• Node.js version: 16.7.0

Prisma Version

prisma                  : 3.8.1
@prisma/client          : 3.8.1
Current platform        : darwin
Query Engine (Node-API) : libquery-engine 34df67547cf5598f5a6cd3eb45f14ee70c3fb86f (at ../../node_modules/@prisma/engines/libquery_engine-darwin.dylib.node)
Migration Engine        : migration-engine-cli 34df67547cf5598f5a6cd3eb45f14ee70c3fb86f (at ../../node_modules/@prisma/engines/migration-engine-darwin)
Introspection Engine    : introspection-core 34df67547cf5598f5a6cd3eb45f14ee70c3fb86f (at ../../node_modules/@prisma/engines/introspection-engine-darwin)
Format Binary           : prisma-fmt 34df67547cf5598f5a6cd3eb45f14ee70c3fb86f (at ../../node_modules/@prisma/engines/prisma-fmt-darwin)
Default Engines Hash    : 34df67547cf5598f5a6cd3eb45f14ee70c3fb86f
Studio                  : 0.452.0
Preview Features        : interactiveTransactions