Connection Pooling increases cost?

[BeGeos]

I was reading the docs on the main website neon.tech and they are very well made. I also stumbled across this the part where Neon offers a serverless driver which helps enable connection pooling to be used effectively with edge functions or cloud workers.

Now, I am not an expert and I haven't tested it directly but I had a small doubt. Now, edge functions are quite popular, we can say they are pretty hot right now, or maybe they are getting a bit colder, but still fairly tepid.

Since Neon is a database service whose cost is based on compute time and usage, wouldn't the use of connection pooling increase the cost? I mean when I create a pool, a connection stays open for longer, therefore I use more computing time. Is Neon mitigating this in any way? or am I right in my estimate about this? I might actually be missing something, as I said I am not an expert on either edge or serverless databases.

Thanks